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expansion</span> </div> </a> <ul id="toc-Structure_of_cosmic_expansion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dynamics_of_cosmic_expansion" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Dynamics_of_cosmic_expansion"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Dynamics of cosmic expansion</span> </div> </a> <ul id="toc-Dynamics_of_cosmic_expansion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Distances_in_the_expanding_universe" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Distances_in_the_expanding_universe"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Distances in the expanding universe</span> </div> </a> <button aria-controls="toc-Distances_in_the_expanding_universe-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Distances in the expanding universe subsection</span> </button> <ul id="toc-Distances_in_the_expanding_universe-sublist" class="vector-toc-list"> <li id="toc-Comoving_coordinates" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Comoving_coordinates"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Comoving coordinates</span> </div> </a> <ul id="toc-Comoving_coordinates-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Shape_of_the_universe" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Shape_of_the_universe"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Shape of the universe</span> </div> </a> <ul id="toc-Shape_of_the_universe-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cosmological_horizons" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cosmological_horizons"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Cosmological horizons</span> </div> </a> <ul id="toc-Cosmological_horizons-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Consequences_of_cosmic_expansion" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Consequences_of_cosmic_expansion"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Consequences of cosmic expansion</span> </div> </a> <button aria-controls="toc-Consequences_of_cosmic_expansion-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Consequences of cosmic expansion subsection</span> </button> <ul id="toc-Consequences_of_cosmic_expansion-sublist" class="vector-toc-list"> <li id="toc-Velocities_and_redshifts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Velocities_and_redshifts"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Velocities and redshifts</span> </div> </a> <ul id="toc-Velocities_and_redshifts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Temperature" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Temperature"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Temperature</span> </div> </a> <ul id="toc-Temperature-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Density" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Density"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Density</span> </div> </a> <ul id="toc-Density-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Expansion_history" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Expansion_history"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Expansion history</span> </div> </a> <button aria-controls="toc-Expansion_history-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Expansion history subsection</span> </button> <ul id="toc-Expansion_history-sublist" class="vector-toc-list"> <li id="toc-Cosmic_inflation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cosmic_inflation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Cosmic inflation</span> </div> </a> <ul id="toc-Cosmic_inflation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Radiation_epoch" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Radiation_epoch"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Radiation epoch</span> </div> </a> <ul id="toc-Radiation_epoch-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Matter_epoch" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Matter_epoch"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Matter epoch</span> </div> </a> <ul id="toc-Matter_epoch-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dark_energy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dark_energy"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Dark energy</span> </div> </a> <ul id="toc-Dark_energy-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Measuring_the_expansion_rate" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Measuring_the_expansion_rate"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Measuring the expansion rate</span> </div> </a> <ul id="toc-Measuring_the_expansion_rate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conceptual_considerations_and_misconceptions" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Conceptual_considerations_and_misconceptions"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Conceptual considerations and misconceptions</span> </div> </a> <button aria-controls="toc-Conceptual_considerations_and_misconceptions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Conceptual considerations and misconceptions subsection</span> </button> <ul id="toc-Conceptual_considerations_and_misconceptions-sublist" class="vector-toc-list"> <li id="toc-Measuring_distances_in_expanding_space" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Measuring_distances_in_expanding_space"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Measuring distances in expanding space</span> </div> </a> <ul id="toc-Measuring_distances_in_expanding_space-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Topology_of_expanding_space" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Topology_of_expanding_space"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Topology of expanding space</span> </div> </a> <ul id="toc-Topology_of_expanding_space-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Density_of_universe_during_expansion" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Density_of_universe_during_expansion"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>Density of universe during expansion</span> </div> </a> <ul id="toc-Density_of_universe_during_expansion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Effects_of_expansion_on_small_scales" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Effects_of_expansion_on_small_scales"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.4</span> <span>Effects of expansion on small scales</span> </div> </a> <ul id="toc-Effects_of_expansion_on_small_scales-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Metric_expansion_and_speed_of_light" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Metric_expansion_and_speed_of_light"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.5</span> <span>Metric expansion and speed of light</span> </div> </a> <ul id="toc-Metric_expansion_and_speed_of_light-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Common_analogies_for_cosmic_expansion" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Common_analogies_for_cosmic_expansion"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.6</span> <span>Common analogies for cosmic expansion</span> </div> </a> <ul id="toc-Common_analogies_for_cosmic_expansion-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Printed_references" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Printed_references"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Printed references</span> </div> </a> <ul id="toc-Printed_references-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Expansion of the universe</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 44 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-44" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">44 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Uitdying_van_die_heelal" title="Uitdying van die heelal – Afrikaans" lang="af" hreflang="af" data-title="Uitdying van die heelal" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%85%D8%AF%D8%AF_%D8%A7%D9%84%D9%83%D9%88%D9%86" title="تمدد الكون – Arabic" lang="ar" hreflang="ar" data-title="تمدد الكون" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kainat%C4%B1n_geni%C5%9Fl%C9%99nm%C9%99si_n%C9%99z%C9%99riyy%C9%99si" title="Kainatın genişlənməsi nəzəriyyəsi – Azerbaijani" lang="az" hreflang="az" data-title="Kainatın genişlənməsi nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A7%8D%E0%A6%A5%E0%A6%BE%E0%A6%A8%E0%A7%87%E0%A6%B0_%E0%A6%AE%E0%A7%87%E0%A6%9F%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%95_%E0%A6%B8%E0%A6%AE%E0%A7%8D%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%B8%E0%A6%BE%E0%A6%B0%E0%A6%A3" title="স্থানের মেট্রিক সম্প্রসারণ – Bangla" lang="bn" hreflang="bn" data-title="স্থানের মেট্রিক সম্প্রসারণ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A0%D0%B0%D1%81%D1%88%D1%8B%D1%80%D1%8D%D0%BD%D0%BD%D0%B5_%D0%A1%D1%83%D1%81%D0%B2%D0%B5%D1%82%D1%83" title="Расшырэнне Сусвету – Belarusian" lang="be" hreflang="be" data-title="Расшырэнне Сусвету" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B7%D1%88%D0%B8%D1%80%D0%B5%D0%BD%D0%B8%D0%B5_%D0%BD%D0%B0_%D0%92%D1%81%D0%B5%D0%BB%D0%B5%D0%BD%D0%B0%D1%82%D0%B0" title="Разширение на Вселената – Bulgarian" lang="bg" hreflang="bg" data-title="Разширение на Вселената" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/%C5%A0irenje_univerzuma" title="Širenje univerzuma – Bosnian" lang="bs" hreflang="bs" data-title="Širenje univerzuma" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Expansi%C3%B3_de_l%27Univers" title="Expansió de l'Univers – Catalan" lang="ca" hreflang="ca" data-title="Expansió de l'Univers" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%C3%87%D1%83%D1%82_%D0%A2%C4%95%D0%BD%D1%87%D0%B5_%D1%81%D0%B0%D1%80%C4%83%D0%BB%D0%BD%D0%B8" title="Çут Тĕнче сарăлни – Chuvash" lang="cv" hreflang="cv" data-title="Çут Тĕнче сарăлни" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Universets_udvidelse" title="Universets udvidelse – Danish" lang="da" hreflang="da" data-title="Universets udvidelse" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Expansion_des_Universums" title="Expansion des Universums – German" lang="de" hreflang="de" data-title="Expansion des Universums" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Universumi_paisumine" title="Universumi paisumine – Estonian" lang="et" hreflang="et" data-title="Universumi paisumine" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%B1%CF%83%CF%84%CE%BF%CE%BB%CE%AE_%CF%84%CE%BF%CF%85_%CF%83%CF%8D%CE%BC%CF%80%CE%B1%CE%BD%CF%84%CE%BF%CF%82" title="Διαστολή του σύμπαντος – Greek" lang="el" hreflang="el" data-title="Διαστολή του σύμπαντος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Expansi%C3%B3n_m%C3%A9trica_del_espacio" title="Expansión métrica del espacio – Spanish" lang="es" hreflang="es" data-title="Expansión métrica del espacio" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Ekspansio_de_la_universo" title="Ekspansio de la universo – Esperanto" lang="eo" hreflang="eo" data-title="Ekspansio de la universo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Unibertsoaren_hedapen_metrikoa" title="Unibertsoaren hedapen metrikoa – Basque" lang="eu" hreflang="eu" data-title="Unibertsoaren hedapen metrikoa" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%86%D8%A8%D8%B3%D8%A7%D8%B7_%D8%AC%D9%87%D8%A7%D9%86" title="انبساط جهان – Persian" lang="fa" hreflang="fa" data-title="انبساط جهان" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Expansion_de_l%27Univers" title="Expansion de l'Univers – French" lang="fr" hreflang="fr" data-title="Expansion de l'Univers" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9A%B0%EC%A3%BC%ED%8C%BD%EC%B0%BD" title="우주팽창 – Korean" lang="ko" hreflang="ko" data-title="우주팽창" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D5%AB%D5%A5%D5%A6%D5%A5%D6%80%D6%84%D5%AB_%D5%A8%D5%B6%D5%A4%D5%AC%D5%A1%D5%B5%D5%B6%D5%B8%D6%82%D5%B4" title="Տիեզերքի ընդլայնում – Armenian" lang="hy" hreflang="hy" data-title="Տիեզերքի ընդլայնում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%82%E0%A4%A1_%E0%A4%95%E0%A4%BE_%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A4%BE%E0%A4%B0" title="ब्रह्मांड का विस्तार – Hindi" lang="hi" hreflang="hi" data-title="ब्रह्मांड का विस्तार" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Perluasan_alam_semesta" title="Perluasan alam semesta – Indonesian" lang="id" hreflang="id" data-title="Perluasan alam semesta" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Espansione_metrica_dello_spazio" title="Espansione metrica dello spazio – Italian" lang="it" hreflang="it" data-title="Espansione metrica dello spazio" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a 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data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Visatos_pl%C4%97timasis" title="Visatos plėtimasis – Lithuanian" lang="lt" hreflang="lt" data-title="Visatos plėtimasis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Metrische_uitdijing_van_de_ruimte" title="Metrische uitdijing van de ruimte – Dutch" lang="nl" hreflang="nl" data-title="Metrische uitdijing van de ruimte" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Expansion_de_l%27Univ%C3%A8rs" title="Expansion de l'Univèrs – Occitan" lang="oc" hreflang="oc" data-title="Expansion de l'Univèrs" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AF_%D9%86%DA%93%DB%8D_%D9%BE%D8%B1%D8%A7%D8%AE%DB%90%D8%AF%D9%86%D9%87_(%D8%A7%D9%86%D8%A8%D8%B3%D8%A7%D8%B7)" title="د نړۍ پراخېدنه (انبساط) – Pashto" lang="ps" hreflang="ps" data-title="د نړۍ پراخېدنه (انبساط)" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Expans%C3%A3o_m%C3%A9trica_do_espa%C3%A7o" title="Expansão métrica do espaço – Portuguese" lang="pt" hreflang="pt" data-title="Expansão métrica do espaço" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Expansiunea_universului" title="Expansiunea universului – Romanian" lang="ro" hreflang="ro" data-title="Expansiunea universului" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D1%81%D1%88%D0%B8%D1%80%D0%B5%D0%BD%D0%B8%D0%B5_%D0%92%D1%81%D0%B5%D0%BB%D0%B5%D0%BD%D0%BD%D0%BE%D0%B9" title="Расширение Вселенной – Russian" lang="ru" hreflang="ru" data-title="Расширение Вселенной" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Rozp%C3%ADnanie_vesm%C3%ADru" 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src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/CMB_Timeline300_no_WMAP.jpg/300px-CMB_Timeline300_no_WMAP.jpg" decoding="async" width="300" height="198" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/CMB_Timeline300_no_WMAP.jpg/450px-CMB_Timeline300_no_WMAP.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/CMB_Timeline300_no_WMAP.jpg/600px-CMB_Timeline300_no_WMAP.jpg 2x" data-file-width="3000" data-file-height="1980" /></a><figcaption>A graphical representation of the expansion of the universe from the <a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a> to the present day, with the inflationary epoch represented as the dramatic expansion seen on the left. This visualization shows only a section of the universe; the empty space outside the diagram should not be taken to represent empty space outside the universe (which does not necessarily exist).</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist 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.sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Physical_cosmology" title="Physical cosmology">Physical cosmology</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:WMAP_2012.png" class="mw-file-description"><img alt="Full-sky image derived from nine years' WMAP data" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/WMAP_2012.png/220px-WMAP_2012.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/WMAP_2012.png/330px-WMAP_2012.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/WMAP_2012.png/440px-WMAP_2012.png 2x" data-file-width="4096" data-file-height="2048" /></a></span></td></tr><tr><td class="sidebar-above" style="border:0;font-weight:normal; display:block;margin-bottom:0.4em;"> <ul><li><a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a> <b>·</b> <a href="/wiki/Universe" title="Universe">Universe</a></li> <li><a href="/wiki/Age_of_the_universe" title="Age of the universe">Age of the universe</a></li> <li><a href="/wiki/Chronology_of_the_universe" title="Chronology of the universe">Chronology of the universe</a></li></ul></td></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)">Early universe</div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Cosmic_inflation" title="Cosmic inflation">Inflation</a> <b>·</b> <a href="/wiki/Big_Bang_nucleosynthesis" title="Big Bang nucleosynthesis">Nucleosynthesis</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-weight:normal;font-style:italic;"> Backgrounds</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Gravitational_wave_background" title="Gravitational wave background">Gravitational wave (GWB)</a></li> <li><a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">Microwave (CMB)</a> <b>·</b> <a href="/wiki/Cosmic_neutrino_background" title="Cosmic neutrino background">Neutrino (CNB)</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)">Expansion <b>·</b> Future</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a> <b>·</b> <a href="/wiki/Redshift" title="Redshift">Redshift</a></li> <li><a class="mw-selflink selflink">Expansion of the universe</a></li> <li><a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">FLRW metric</a> <b>·</b> <a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann equations</a></li> <li><a href="/wiki/Inhomogeneous_cosmology" title="Inhomogeneous cosmology">Inhomogeneous cosmology</a></li> <li><a href="/wiki/Future_of_an_expanding_universe" title="Future of an expanding universe">Future of an expanding universe</a></li> <li><a href="/wiki/Ultimate_fate_of_the_universe" title="Ultimate fate of the universe">Ultimate fate of the universe</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)">Components <b>·</b> Structure</div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-weight:normal;font-style:italic;"> Components</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a></li> <li><a href="/wiki/Dark_energy" title="Dark energy">Dark energy</a> <b>·</b> <a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-weight:normal;font-style:italic;"> Structure</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Shape_of_the_universe" title="Shape of the universe">Shape of the universe</a></li> <li><a href="/wiki/Galaxy_filament" title="Galaxy filament">Galaxy filament</a> <b>·</b> <a href="/wiki/Galaxy_formation_and_evolution" title="Galaxy formation and evolution">Galaxy formation</a></li> <li><a href="/wiki/Large_quasar_group" title="Large quasar group">Large quasar group</a></li> <li><a href="/wiki/Observable_universe#Large-scale_structure" title="Observable universe">Large-scale structure</a></li> <li><a href="/wiki/Reionization" title="Reionization">Reionization</a> <b>·</b> <a href="/wiki/Structure_formation" title="Structure formation">Structure formation</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)"><a href="/wiki/Observational_cosmology" title="Observational cosmology">Experiments</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Black_Hole_Initiative" title="Black Hole Initiative">Black Hole Initiative (BHI)</a></li> <li><a href="/wiki/BOOMERanG_experiment" title="BOOMERanG experiment">BOOMERanG</a></li> <li><a href="/wiki/Cosmic_Background_Explorer" title="Cosmic Background Explorer">Cosmic Background Explorer (COBE)</a></li> <li><a href="/wiki/Dark_Energy_Survey" title="Dark Energy Survey">Dark Energy Survey</a></li> <li><a href="/wiki/Planck_(spacecraft)" title="Planck (spacecraft)">Planck space observatory</a></li> <li><a href="/wiki/Sloan_Digital_Sky_Survey" title="Sloan Digital Sky Survey">Sloan Digital Sky Survey (SDSS)</a></li> <li><a href="/wiki/2dF_Galaxy_Redshift_Survey" title="2dF Galaxy Redshift Survey">2dF Galaxy Redshift Survey ("2dF")</a></li> <li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><a href="/wiki/Wilkinson_Microwave_Anisotropy_Probe" title="Wilkinson Microwave Anisotropy Probe">Wilkinson Microwave Anisotropy<br />Probe (WMAP)</a></div></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist" style="padding:0 0.9em;"> <ul><li><a href="/wiki/Marc_Aaronson" title="Marc Aaronson">Aaronson</a></li> <li><a href="/wiki/Hannes_Alfv%C3%A9n" title="Hannes Alfvén">Alfvén</a></li> <li><a href="/wiki/Ralph_Alpher" title="Ralph Alpher">Alpher</a></li> <li><a href="/wiki/Nicolaus_Copernicus" title="Nicolaus Copernicus">Copernicus</a></li> <li><a href="/wiki/Willem_de_Sitter" title="Willem de Sitter">de Sitter</a></li> <li><a href="/wiki/Robert_H._Dicke" title="Robert H. Dicke">Dicke</a></li> <li><a href="/wiki/J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/George_F._R._Ellis" title="George F. R. Ellis">Ellis</a></li> <li><a href="/wiki/Alexander_Friedmann" title="Alexander Friedmann">Friedmann</a></li> <li><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a></li> <li><a href="/wiki/George_Gamow" title="George Gamow">Gamow</a></li> <li><a href="/wiki/Alan_Guth" title="Alan Guth">Guth</a></li> <li><a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Hawking</a></li> <li><a href="/wiki/Edwin_Hubble" title="Edwin Hubble">Hubble</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a></li> <li><a href="/wiki/Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li> <li><a href="/wiki/John_C._Mather" title="John C. Mather">Mather</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Roger_Penrose" title="Roger Penrose">Penrose</a></li> <li><a href="/wiki/Arno_Allan_Penzias" title="Arno Allan Penzias">Penzias</a></li> <li><a href="/wiki/Vera_Rubin" title="Vera Rubin">Rubin</a></li> <li><a href="/wiki/Brian_Schmidt" title="Brian Schmidt">Schmidt</a></li> <li><a href="/wiki/George_Smoot" title="George Smoot">Smoot</a></li> <li><a href="/wiki/Nicholas_B._Suntzeff" title="Nicholas B. Suntzeff">Suntzeff</a></li> <li><a href="/wiki/Rashid_Sunyaev" title="Rashid Sunyaev">Sunyaev</a></li> <li><a href="/wiki/Richard_C._Tolman" title="Richard C. Tolman">Tolman</a></li> <li><a href="/wiki/Robert_Woodrow_Wilson" title="Robert Woodrow Wilson">Wilson</a></li> <li><a href="/wiki/Yakov_Zeldovich" title="Yakov Zeldovich">Zeldovich</a></li></ul> </div> <ul><li><a href="/wiki/List_of_cosmologists" title="List of cosmologists">List of cosmologists</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)"><a href="/wiki/Physical_cosmology#Subject_history" title="Physical cosmology">Subject history</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><a href="/wiki/Discovery_of_cosmic_microwave_background_radiation" title="Discovery of cosmic microwave background radiation">Discovery of cosmic microwave<br />background radiation</a></div></li> <li><a href="/wiki/History_of_the_Big_Bang_theory" title="History of the Big Bang theory">History of the Big Bang theory</a></li> <li><a href="/wiki/Timeline_of_cosmological_theories" title="Timeline of cosmological theories">Timeline of cosmological theories</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below" style="display:block;margin-top:0.4em; line-height:1.6em;padding-bottom:0.5em;"> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Physical_cosmology" title="Category:Physical cosmology">Category</a></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/16px-Crab_Nebula.jpg" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/24px-Crab_Nebula.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/32px-Crab_Nebula.jpg 2x" data-file-width="3864" data-file-height="3864" /></span></span> </span><a href="/wiki/Portal:Astronomy" title="Portal:Astronomy">Astronomy portal</a></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Physical_cosmology" title="Template:Physical cosmology"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Physical_cosmology" title="Template talk:Physical cosmology"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Physical_cosmology" title="Special:EditPage/Template:Physical cosmology"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The <b>expansion of the universe</b> is the increase in <a href="/wiki/Proper_length" title="Proper length">distance</a> between <a href="/wiki/Gravitational_binding_energy" title="Gravitational binding energy">gravitationally unbound</a> parts of the <a href="/wiki/Observable_universe" title="Observable universe">observable universe</a> with time.<sup id="cite_ref-NYT-20170220_1-0" class="reference"><a href="#cite_note-NYT-20170220-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It is an <a href="/wiki/Intrinsic_and_extrinsic_properties_(philosophy)" title="Intrinsic and extrinsic properties (philosophy)">intrinsic</a> expansion, so it does not mean that the universe expands "into" anything or that space exists "outside" it. To any observer in the universe, it appears that all but <a href="/wiki/Local_Group" title="Local Group">the nearest galaxies</a> (which are bound to each other by gravity) move away at <a href="/wiki/Hubble%27s_law" title="Hubble's law">speeds that are proportional to their distance from the observer</a>, on average. While objects cannot move <a href="/wiki/Faster-than-light" title="Faster-than-light">faster than light</a>, this limitation applies only with respect to <a href="/wiki/Principle_of_locality" title="Principle of locality">local</a> <a href="/wiki/Reference_frame" class="mw-redirect" title="Reference frame">reference frames</a> and does not limit the recession rates of cosmologically distant objects. </p><p>Cosmic expansion is a key feature of <a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a> cosmology. It can be modeled mathematically with the <a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">Friedmann–Lemaître–Robertson–Walker metric</a> (FLRW), where it corresponds to an increase in the scale of the spatial part of the universe's <a href="/wiki/Spacetime" title="Spacetime">spacetime</a> <a href="/wiki/Metric_tensor_(general_relativity)" title="Metric tensor (general relativity)">metric tensor</a> (which governs the size and geometry of spacetime). Within this framework, the separation of objects over time is associated with the expansion of space itself. However, this is not a <a href="/wiki/General_covariance" title="General covariance">generally covariant</a> description but rather only a choice of <a href="/wiki/Coordinate_conditions" title="Coordinate conditions">coordinates</a>. Contrary to common misconception, it is equally valid to adopt a description in which space does not expand and objects simply move apart while under the influence of their mutual gravity.<sup id="cite_ref-arXiv:0809.4573_2-0" class="reference"><a href="#cite_note-arXiv:0809.4573-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-arXiv:0808.1081_3-0" class="reference"><a href="#cite_note-arXiv:0808.1081-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-arXiv:1605.08634_4-0" class="reference"><a href="#cite_note-arXiv:1605.08634-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Although cosmic expansion is often framed as a consequence of <a href="/wiki/General_relativity" title="General relativity">general relativity</a>, it is also predicted by <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newtonian gravity</a>.<sup id="cite_ref-10.1093/mnras/282.1.206_5-0" class="reference"><a href="#cite_note-10.1093/mnras/282.1.206-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-arXiv:1308.1852_6-0" class="reference"><a href="#cite_note-arXiv:1308.1852-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>According to <a href="/wiki/Inflation_(cosmology)" class="mw-redirect" title="Inflation (cosmology)">inflation theory</a>, the universe suddenly expanded during the <a href="/wiki/Inflationary_epoch" title="Inflationary epoch">inflationary epoch</a> (about 10<sup>−32</sup> of a second after the Big Bang), and its volume increased by a factor of at least 10<sup>78</sup> (an expansion of distance by a factor of at least 10<sup>26</sup> in each of the three dimensions). This would be equivalent to expanding an object 1 <a href="/wiki/Nanometer" class="mw-redirect" title="Nanometer">nanometer</a> across (<span class="nowrap"><span data-sort-value="6991100000000000000♠"></span>10<sup>−9</sup> m</span>, about half the width of a <a href="/wiki/Molecule" title="Molecule">molecule</a> of <a href="/wiki/DNA" title="DNA">DNA</a>) to one approximately 10.6 <a href="/wiki/Light-years" class="mw-redirect" title="Light-years">light-years</a> across (about <span class="nowrap"><span data-sort-value="7017100000000000000♠"></span>10<sup>17</sup> m</span>, or 62 trillion miles). Cosmic expansion subsequently decelerated to much slower rates, until around 9.8 billion years after the Big Bang (4 billion years ago) it began to gradually <a href="/wiki/Accelerating_expansion_of_the_universe" title="Accelerating expansion of the universe">expand more quickly</a>, and is still doing so. Physicists have postulated the existence of <a href="/wiki/Dark_energy" title="Dark energy">dark energy</a>, appearing as a <a href="/wiki/Cosmological_constant" title="Cosmological constant">cosmological constant</a> in the simplest gravitational models, as a way to explain this late-time acceleration. According to the simplest extrapolation of the currently favored cosmological model, the <a href="/wiki/Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a>, this acceleration becomes dominant in the future. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1912–1914, <a href="/wiki/Vesto_Slipher" title="Vesto Slipher">Vesto Slipher</a> discovered that light from remote galaxies was <a href="/wiki/Redshift" title="Redshift">redshifted</a>,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> a phenomenon <a href="/wiki/Great_Debate_(astronomy)" title="Great Debate (astronomy)">later</a> interpreted as galaxies receding from the Earth. In 1922, <a href="/wiki/Alexander_Friedmann" title="Alexander Friedmann">Alexander Friedmann</a> used the <a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a> to provide theoretical evidence that the universe is expanding.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Swedish astronomer <a href="/wiki/Knut_Lundmark" title="Knut Lundmark">Knut Lundmark</a> was the first person to find observational evidence for expansion, in 1924. According to Ian Steer of the NASA/IPAC Extragalactic Database of Galaxy Distances, "Lundmark's extragalactic distance estimates were far more accurate than Hubble's, consistent with an expansion rate (Hubble constant) that was within 1% of the best measurements today."<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>In 1927, <a href="/wiki/Georges_Lema%C3%AEtre" title="Georges Lemaître">Georges Lemaître</a> independently reached a similar conclusion to Friedmann on a theoretical basis, and also presented observational evidence for a <a href="/wiki/Hubble%27s_law" title="Hubble's law">linear relationship between distance to galaxies and their recessional velocity</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Edwin_Hubble" title="Edwin Hubble">Edwin Hubble</a> observationally confirmed Lundmark's and Lemaître's findings in 1929.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Assuming the <a href="/wiki/Cosmological_principle" title="Cosmological principle">cosmological principle</a>, these findings would imply that all galaxies are moving away from each other. </p><p>Astronomer <a href="/wiki/Walter_Baade" title="Walter Baade">Walter Baade</a> recalculated the size of the known universe in the 1940s, doubling the previous calculation made by <a href="/wiki/Edwin_Hubble" title="Edwin Hubble">Hubble</a> in 1929.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> He announced this finding to considerable astonishment at the 1952 meeting of the <a href="/wiki/International_Astronomical_Union" title="International Astronomical Union">International Astronomical Union</a> in Rome. For most of the second half of the 20th century, the value of the Hubble constant was estimated to be between <span class="nowrap"><span data-sort-value="7001500000000000000♠"></span>50 and 90 km⋅s<sup>−1</sup>⋅<a href="/wiki/Parsec#Megaparsecs_and_gigaparsecs" title="Parsec">Mpc</a><sup>−1</sup></span>. </p><p>On 13 January 1994, NASA formally announced a completion of its repairs related to the main mirror of the <a href="/wiki/Hubble_Space_Telescope" title="Hubble Space Telescope">Hubble Space Telescope</a>, allowing for sharper images and, consequently, more accurate analyses of its observations.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Shortly after the repairs were made, <a href="/wiki/Wendy_Freedman" title="Wendy Freedman">Wendy Freedman</a>'s 1994 Key Project analyzed the recession velocity of <a href="/wiki/Messier_100" title="Messier 100">M100</a> from the core of the <a href="/wiki/Virgo_Cluster" title="Virgo Cluster">Virgo Cluster</a>, offering a <a href="/wiki/Hubble_constant" class="mw-redirect" title="Hubble constant">Hubble constant</a> measurement of <span class="nowrap"><span data-sort-value="7001800000000000000♠"></span>80<span style="margin-left:0.3em;margin-right:0.15em;">±</span>17 km⋅s<sup>−1</sup>⋅Mpc<sup>−1</sup></span>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Later the same year, <a href="/wiki/Adam_Riess" title="Adam Riess">Adam Riess</a> et al. used an empirical method of <a href="/wiki/Visible_spectrum" title="Visible spectrum">visual-band</a> <a href="/wiki/Light_curve" title="Light curve">light-curve</a> shapes to more finely estimate the <a href="/wiki/Luminosity" title="Luminosity">luminosity</a> of <a href="/wiki/Type_Ia_supernova" title="Type Ia supernova">Type Ia supernovae</a>. This further minimized the systematic <a href="/wiki/Observational_error" title="Observational error">measurement errors</a> of the Hubble constant, to <span class="nowrap"><span data-sort-value="7001670000000000000♠"></span>67<span style="margin-left:0.3em;margin-right:0.15em;">±</span>7 km⋅s<sup>−1</sup>⋅Mpc<sup>−1</sup></span>. Reiss's measurements on the recession velocity of the nearby Virgo Cluster more closely agree with subsequent and independent analyses of <a href="/wiki/Cepheid_variable" title="Cepheid variable">Cepheid variable</a> calibrations of <a href="/wiki/Type_Ia_supernova" title="Type Ia supernova">Type Ia supernova</a>, which estimates a Hubble constant of <span class="nowrap"><span data-sort-value="7001730000000000000♠"></span>73<span style="margin-left:0.3em;margin-right:0.15em;">±</span>7 km⋅s<sup>−1</sup>⋅Mpc<sup>−1</sup></span>.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> In 2003, <a href="/wiki/David_Spergel" title="David Spergel">David Spergel</a>'s analysis of the <a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> during the first year observations of the <i><a href="/wiki/Wilkinson_Microwave_Anisotropy_Probe" title="Wilkinson Microwave Anisotropy Probe">Wilkinson Microwave Anisotropy Probe</a></i> satellite (WMAP) further agreed with the estimated expansion rates for local galaxies, <span class="nowrap"><span data-sort-value="7001720000000000000♠"></span>72<span style="margin-left:0.3em;margin-right:0.15em;">±</span>5 km⋅s<sup>−1</sup>⋅Mpc<sup>−1</sup></span>.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Structure_of_cosmic_expansion">Structure of cosmic expansion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=2" title="Edit section: Structure of cosmic expansion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The universe at the largest scales is observed to be <a href="/wiki/Homogeneity_(physics)" title="Homogeneity (physics)">homogeneous</a> (the same everywhere) and <a href="/wiki/Isotropic" class="mw-redirect" title="Isotropic">isotropic</a> (the same in all directions), consistent with the <a href="/wiki/Cosmological_principle" title="Cosmological principle">cosmological principle</a>. These constraints demand that any expansion of the universe accord with <a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a>, in which objects recede from each observer with velocities proportional to their positions with respect to that observer. That is, recession velocities <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85820588abd7333ef4d0c56539cb31c20e730753" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.175ex; height:2.343ex;" alt="{\displaystyle {\vec {v}}}"></span> scale with (observer-centered) positions <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db2dc6ced9cc3bc7e8b9f2707cbec033f6d3759c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:2.343ex;" alt="{\displaystyle {\vec {x}}}"></span> according to </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {v}}=H{\vec {x}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}=H{\vec {x}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17b2c66c6d1ccc28f9fc73a01681aee888679c48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.314ex; height:2.676ex;" alt="{\displaystyle {\vec {v}}=H{\vec {x}},}"></span></dd></dl> <p>where the Hubble rate <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle H}"></span> quantifies the rate of expansion. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle H}"></span> is a function of <a href="/wiki/Cosmic_time" title="Cosmic time">cosmic time</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Dynamics_of_cosmic_expansion">Dynamics of cosmic expansion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=3" title="Edit section: Dynamics of cosmic expansion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Evolution_of_the_universe.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Evolution_of_the_universe.svg/400px-Evolution_of_the_universe.svg.png" decoding="async" width="400" height="230" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Evolution_of_the_universe.svg/600px-Evolution_of_the_universe.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/Evolution_of_the_universe.svg/800px-Evolution_of_the_universe.svg.png 2x" data-file-width="1486" data-file-height="854" /></a><figcaption>The expansion history depends on the density of the universe. Ω on this graph corresponds to the ratio of the matter density to the <a href="/wiki/Density_parameter" class="mw-redirect" title="Density parameter">critical density</a>, for a matter-dominated universe. The "acceleration" curve shows the trajectory of the scale factor for a universe with dark energy.</figcaption></figure> <p>The expansion of the universe can be understood as a consequence of an initial impulse (possibly due to <a href="/wiki/Inflation_(cosmology)" class="mw-redirect" title="Inflation (cosmology)">inflation</a>), which sent the contents of the universe flying apart. The mutual gravitational attraction of the matter and radiation within the universe gradually slows this expansion over time, but expansion nevertheless continues due to momentum left over from the initial impulse. Also, certain exotic <a href="/wiki/Perfect_fluid" title="Perfect fluid">relativistic fluids</a>, such as <a href="/wiki/Dark_energy" title="Dark energy">dark energy</a> and inflation, exert gravitational repulsion in the cosmological context, which accelerates the expansion of the universe. A <a href="/wiki/Cosmological_constant" title="Cosmological constant">cosmological constant</a> also has this effect. </p><p>Mathematically, the expansion of the universe is quantified by the <a href="/wiki/Scale_factor_(cosmology)" title="Scale factor (cosmology)">scale factor</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>, which is proportional to the average separation between objects, such as galaxies. The scale factor is a function of time and is conventionally set to be <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6104442ed30596ef4d7795d3186273f68d796ea4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.491ex; height:2.176ex;" alt="{\displaystyle a=1}"></span> at the present time. Because the universe is expanding, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> is smaller in the past and larger in the future. Extrapolating back in time with certain cosmological models will yield a moment when the scale factor was zero; our current understanding of cosmology sets <a href="/wiki/Age_of_the_universe" title="Age of the universe">this time at 13.787 ± 0.020 billion years ago</a>. If the universe continues to expand forever, the scale factor will approach infinity in the future. It is also possible in principle for the universe to stop expanding and begin to contract, which corresponds to the scale factor decreasing in time. </p><p>The scale factor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> is a parameter of the <a href="/wiki/FLRW_metric" class="mw-redirect" title="FLRW metric">FLRW metric</a>, and its time evolution is governed by the <a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann equations</a>. The second Friedmann equation, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\ddot {a}}{a}}=-{\frac {4\pi G}{3}}\left(\rho +{\frac {3p}{c^{2}}}\right)+{\frac {\Lambda c^{2}}{3}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>¨</mo> </mover> </mrow> <mi>a</mi> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> <mi>G</mi> </mrow> <mn>3</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mi>ρ</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mi>p</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Λ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>3</mn> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\ddot {a}}{a}}=-{\frac {4\pi G}{3}}\left(\rho +{\frac {3p}{c^{2}}}\right)+{\frac {\Lambda c^{2}}{3}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11bf3e16e2d2015acc475bcba089155133e3f49c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.146ex; height:6.343ex;" alt="{\displaystyle {\frac {\ddot {a}}{a}}=-{\frac {4\pi G}{3}}\left(\rho +{\frac {3p}{c^{2}}}\right)+{\frac {\Lambda c^{2}}{3}},}"></span></dd></dl> <p>shows how the contents of the universe influence its expansion rate. Here, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> is the <a href="/wiki/Gravitational_constant" title="Gravitational constant">gravitational constant</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> is the <a href="/wiki/Energy_density" title="Energy density">energy density</a> within the universe, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> is the <a href="/wiki/Pressure" title="Pressure">pressure</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> is the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac0a4a98a414e3480335f9ba652d12571ec6733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.613ex; height:2.176ex;" alt="{\displaystyle \Lambda }"></span> is the cosmological constant. A positive energy density leads to deceleration of the expansion, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ddot {a}}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>¨</mo> </mover> </mrow> </mrow> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ddot {a}}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcbc627f5fae1603bd12ba7afbea495932fb5027" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.491ex; height:2.176ex;" alt="{\displaystyle {\ddot {a}}<0}"></span>, and a positive pressure further decelerates expansion. On the other hand, sufficiently negative pressure with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p<-\rho c^{2}/3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo><</mo> <mo>−</mo> <mi>ρ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p<-\rho c^{2}/3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9daded5a24a5b4174bb9f97b6f09e6622a7c0bf3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:11.753ex; height:3.176ex;" alt="{\displaystyle p<-\rho c^{2}/3}"></span> leads to accelerated expansion, and the cosmological constant also accelerates expansion. <a href="/wiki/Nonrelativistic" class="mw-redirect" title="Nonrelativistic">Nonrelativistic</a> <a href="/wiki/Matter" title="Matter">matter</a> is essentially pressureless, with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |p|\ll \rho c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>≪</mo> <mi>ρ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |p|\ll \rho c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd786147baa66bd0229936cb95db49f9b33af275" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.34ex; height:3.176ex;" alt="{\displaystyle |p|\ll \rho c^{2}}"></span>, while a gas of <a href="/wiki/Ultrarelativistic" class="mw-redirect" title="Ultrarelativistic">ultrarelativistic</a> particles (such as a <a href="/wiki/Photon_gas" title="Photon gas">photon gas</a>) has positive pressure <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=\rho c^{2}/3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>ρ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=\rho c^{2}/3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41277d83ad6a5bd7f4fb1cc6c0559de967e632f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:9.945ex; height:3.176ex;" alt="{\displaystyle p=\rho c^{2}/3}"></span>. Negative-pressure fluids, like dark energy, are not experimentally confirmed, but the existence of dark energy is inferred from astronomical observations. </p><p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Distances_in_the_expanding_universe">Distances in the expanding universe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=4" title="Edit section: Distances in the expanding universe"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Comoving_coordinates">Comoving coordinates</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=5" title="Edit section: Comoving coordinates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Comoving_coordinates" class="mw-redirect" title="Comoving coordinates">Comoving coordinates</a></div> <p>In an expanding universe, it is often useful to study the evolution of <a href="/wiki/Large-scale_structure_of_the_universe" class="mw-redirect" title="Large-scale structure of the universe">structure</a> with the expansion of the universe factored out. This motivates the use of <a href="/wiki/Comoving_coordinates" class="mw-redirect" title="Comoving coordinates">comoving coordinates</a>, which are defined to grow proportionally with the scale factor. If an object is moving only with the <a href="/wiki/Hubble_flow" class="mw-redirect" title="Hubble flow">Hubble flow</a> of the expanding universe, with no other motion, then it remains stationary in comoving coordinates. The comoving coordinates are the spatial coordinates in the <a href="/wiki/FLRW_metric" class="mw-redirect" title="FLRW metric">FLRW metric</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Shape_of_the_universe">Shape of the universe</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=6" title="Edit section: Shape of the universe"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Shape_of_the_universe" title="Shape of the universe">Shape of the universe</a></div> <p>The universe is a four-dimensional spacetime, but within a universe that obeys the cosmological principle, there is a natural choice of three-dimensional spatial surface. These are the surfaces on which observers who are stationary in comoving coordinates agree on the <a href="/wiki/Age_of_the_universe" title="Age of the universe">age of the universe</a>. In a universe governed by <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>, such surfaces would be <a href="/wiki/Hyperboloid" title="Hyperboloid">hyperboloids</a>, because relativistic <a href="/wiki/Time_dilation" title="Time dilation">time dilation</a> means that rapidly receding distant observers' clocks are slowed, so that spatial surfaces must bend "into the future" over long distances. However, within <a href="/wiki/General_relativity" title="General relativity">general relativity</a>, the shape of these <i>comoving synchronous</i> spatial surfaces is affected by gravity. Current observations are consistent with these spatial surfaces being geometrically flat (so that, for example, the angles of a triangle add up to 180 degrees). </p> <div class="mw-heading mw-heading3"><h3 id="Cosmological_horizons">Cosmological horizons</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=7" title="Edit section: Cosmological horizons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Cosmological_horizon" title="Cosmological horizon">Cosmological horizon</a></div> <p>An expanding universe typically has a finite age. Light, and other particles, can have propagated only a finite distance. The comoving distance that such particles can have covered over the age of the universe is known as the <a href="/wiki/Particle_horizon" title="Particle horizon">particle horizon</a>, and the region of the universe that lies within our particle horizon is known as the <a href="/wiki/Observable_universe" title="Observable universe">observable universe</a>. </p><p>If the dark energy that is inferred to dominate the universe today is a cosmological constant, then the particle horizon converges to a finite value in the infinite future. This implies that the amount of the universe that we will ever be able to observe is limited. Many systems exist whose light can never reach us, because there is a <a href="/wiki/Cosmic_event_horizon" class="mw-redirect" title="Cosmic event horizon">cosmic event horizon</a> induced by the repulsive gravity of the dark energy. </p><p>Within the study of the evolution of structure within the universe, a natural scale emerges, known as the <a href="/wiki/Hubble_horizon" class="mw-redirect" title="Hubble horizon">Hubble horizon</a>. <a href="/wiki/Cosmological_perturbation_theory" title="Cosmological perturbation theory">Cosmological perturbations</a> much larger than the Hubble horizon are not dynamical, because gravitational influences do not have time to propagate across them, while perturbations much smaller than the Hubble horizon are straightforwardly governed by <a href="/wiki/Newtonian_gravity" class="mw-redirect" title="Newtonian gravity">Newtonian gravitational dynamics</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Consequences_of_cosmic_expansion">Consequences of cosmic expansion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=8" title="Edit section: Consequences of cosmic expansion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Velocities_and_redshifts">Velocities and redshifts</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=9" title="Edit section: Velocities and redshifts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An object's <a href="/wiki/Peculiar_velocity" title="Peculiar velocity">peculiar velocity</a> is its velocity with respect to the comoving coordinate grid, i.e., with respect to the average expansion-associated motion of the surrounding material. It is a measure of how a particle's motion deviates from the <a href="/wiki/Hubble_flow" class="mw-redirect" title="Hubble flow">Hubble flow</a> of the expanding universe. The peculiar velocities of nonrelativistic particles decay as the universe expands, in inverse proportion with the cosmic <a href="/wiki/Scale_factor" class="mw-redirect" title="Scale factor">scale factor</a>. This can be understood as a self-sorting effect. A particle that is moving in some direction gradually overtakes the Hubble flow of cosmic expansion in that direction, asymptotically approaching material with the same velocity as its own. </p><p>More generally, the peculiar <a href="/wiki/Momentum" title="Momentum">momenta</a> of both relativistic and nonrelativistic particles decay in inverse proportion with the scale factor. For photons, this leads to the <a href="/wiki/Cosmological_redshift" class="mw-redirect" title="Cosmological redshift">cosmological redshift</a>. While the cosmological redshift is often explained as the stretching of photon wavelengths due to "expansion of space", it is more naturally viewed as a consequence of the <a href="/wiki/Doppler_effect" title="Doppler effect">Doppler effect</a>.<sup id="cite_ref-arXiv:0808.1081_3-1" class="reference"><a href="#cite_note-arXiv:0808.1081-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Temperature">Temperature</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=10" title="Edit section: Temperature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The universe cools as it expands. This follows from the decay of particles' peculiar momenta, as discussed above. It can also be understood as <a href="/wiki/Adiabatic_cooling" class="mw-redirect" title="Adiabatic cooling">adiabatic cooling</a>. The temperature of <a href="/wiki/Ultrarelativistic" class="mw-redirect" title="Ultrarelativistic">ultrarelativistic</a> fluids, often called "radiation" and including the <a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a>, scales inversely with the scale factor (i.e. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\propto a^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>∝</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\propto a^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc532fc3a547fda9be1d96d15bcfb22eb7a29f86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.297ex; height:2.676ex;" alt="{\displaystyle T\propto a^{-1}}"></span>). The temperature of nonrelativistic matter drops more sharply, scaling as the inverse square of the scale factor (i.e. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\propto a^{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>∝</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\propto a^{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cbe0066137b81227666df4696e0719d8404891e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.297ex; height:2.676ex;" alt="{\displaystyle T\propto a^{-2}}"></span>). </p> <div class="mw-heading mw-heading3"><h3 id="Density">Density</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=11" title="Edit section: Density"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The contents of the universe dilute as it expands. The number of particles within a comoving volume remains fixed (on average), while the volume expands. For nonrelativistic matter, this implies that the energy density drops as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho \propto a^{-3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>∝</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho \propto a^{-3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a10aa0b387441378ec13f5bc88a5a629afaef679" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.863ex; height:3.176ex;" alt="{\displaystyle \rho \propto a^{-3}}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> is the <a href="/wiki/Scale_factor" class="mw-redirect" title="Scale factor">scale factor</a>. </p><p>For ultrarelativistic particles ("radiation"), the energy density drops more sharply, as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho \propto a^{-4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>∝</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho \propto a^{-4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d5f48a476b8fd8a18e805ace8e695c04eca8d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.863ex; height:3.176ex;" alt="{\displaystyle \rho \propto a^{-4}}"></span>. This is because in addition to the volume dilution of the particle count, the energy of each particle (including the <a href="/wiki/Rest_mass_energy" class="mw-redirect" title="Rest mass energy">rest mass energy</a>) also drops significantly due to the decay of peculiar momenta. </p><p>In general, we can consider a <a href="/wiki/Perfect_fluid" title="Perfect fluid">perfect fluid</a> with pressure <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=w\rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>w</mi> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=w\rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60ea24a71ed84815ba600571ee579ce4f21c3b61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:7.223ex; height:2.176ex;" alt="{\displaystyle p=w\rho }"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> is the energy density. The parameter <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}"></span> is the <a href="/wiki/Equation_of_state_(cosmology)" title="Equation of state (cosmology)">equation of state parameter</a>. The energy density of such a fluid drops as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho \propto a^{-3(1+w)}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>∝</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>w</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho \propto a^{-3(1+w)}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb61280c1173faca372104b29bb06ab19cde87da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.066ex; height:3.343ex;" alt="{\displaystyle \rho \propto a^{-3(1+w)}.}"></span></dd></dl> <p>Nonrelativistic matter has <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9bb71c9fa0018f0752a2384a7ab9f1c2b628771e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.925ex; height:2.176ex;" alt="{\displaystyle w=0}"></span> while radiation has <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w=1/3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w=1/3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5920c43ddd99ecaa1aa5c530019693577a34ee88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.25ex; height:2.843ex;" alt="{\displaystyle w=1/3}"></span>. For an exotic fluid with negative pressure, like dark energy, the energy density drops more slowly; if <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w=-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w=-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0dc6e8ffa1ebcf4456ba3b4e1c79f0ca92fba76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.733ex; height:2.343ex;" alt="{\displaystyle w=-1}"></span> it remains constant in time. If <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w<-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo><</mo> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w<-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e333dc6e937a422df8dd26a3f4af82c91a2f415" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.733ex; height:2.343ex;" alt="{\displaystyle w<-1}"></span>, corresponding to <a href="/wiki/Phantom_energy" title="Phantom energy">phantom energy</a>, the energy density grows as the universe expands. </p> <div class="mw-heading mw-heading2"><h2 id="Expansion_history">Expansion history</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=12" title="Edit section: Expansion history"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Cosmic_inflation">Cosmic inflation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=13" title="Edit section: Cosmic inflation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Inflation_(cosmology)" class="mw-redirect" title="Inflation (cosmology)">inflation (cosmology)</a> and <a href="/wiki/Inflaton" title="Inflaton">inflaton</a></div> <p>Inflation is a period of accelerated expansion hypothesized to have occurred at a time of around 10<sup>−32</sup> seconds. It would have been driven by the <a href="/wiki/Inflaton" title="Inflaton">inflaton</a>, a <a href="/wiki/Field_(physics)" title="Field (physics)">field</a> that has a positive-energy <a href="/wiki/False_vacuum" title="False vacuum">false vacuum</a> state. Inflation was originally proposed to explain the absence of exotic relics predicted by <a href="/wiki/Grand_unified_theories" class="mw-redirect" title="Grand unified theories">grand unified theories</a>, such as <a href="/wiki/Magnetic_monopoles" class="mw-redirect" title="Magnetic monopoles">magnetic monopoles</a>, because the rapid expansion would have diluted such relics. It was subsequently realized that the accelerated expansion would also solve the <a href="/wiki/Horizon_problem" title="Horizon problem">horizon problem</a> and the <a href="/wiki/Flatness_problem" title="Flatness problem">flatness problem</a>. Additionally, <a href="/wiki/Quantum_fluctuation" title="Quantum fluctuation">quantum fluctuations</a> during inflation would have created initial variations in the density of the universe, which gravity later amplified to yield the observed <a href="/wiki/Matter_power_spectrum" title="Matter power spectrum">spectrum of matter density variations</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2024)">citation needed</span></a></i>]</sup> </p><p>During inflation, the cosmic <a href="/wiki/Scale_factor_(cosmology)" title="Scale factor (cosmology)">scale factor</a> grew exponentially in time. In order to solve the horizon and flatness problems, inflation must have lasted long enough that the scale factor grew by at least a factor of e<sup>60</sup> (about 10<sup>26</sup>).<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2024)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Radiation_epoch">Radiation epoch</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=14" title="Edit section: Radiation epoch"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The history of the universe after inflation but before a time of about 1 second is largely unknown.<sup id="cite_ref-arXiv:2006.16182_20-0" class="reference"><a href="#cite_note-arXiv:2006.16182-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> However, the universe is known to have been dominated by ultrarelativistic <a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a> particles, conventionally called <i>radiation</i>, by the time of <a href="/wiki/Neutrino_decoupling" title="Neutrino decoupling">neutrino decoupling</a> at about 1 second.<sup id="cite_ref-arXiv:1511.00672_21-0" class="reference"><a href="#cite_note-arXiv:1511.00672-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> During radiation domination, cosmic expansion decelerated, with the scale factor growing proportionally with the square root of the time. </p> <div class="mw-heading mw-heading3"><h3 id="Matter_epoch">Matter epoch</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=15" title="Edit section: Matter epoch"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since radiation <a href="/wiki/Redshift" title="Redshift">redshifts</a> as the universe expands, eventually nonrelativistic <a href="/wiki/Matter" title="Matter">matter</a> came to dominate the energy density of the universe. This transition happened at a time of about 50 thousand years after the Big Bang. During the matter-dominated epoch, cosmic expansion also decelerated, with the scale factor growing as the 2/3 power of the time (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\propto t^{2/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∝</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\propto t^{2/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f946d37f401a6029a8aa06dd648489ccb5d83ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.866ex; height:2.843ex;" alt="{\displaystyle a\propto t^{2/3}}"></span>). Also, gravitational structure formation is most efficient when nonrelativistic matter dominates, and this epoch is responsible for the formation of <a href="/wiki/Galaxies" class="mw-redirect" title="Galaxies">galaxies</a> and the <a href="/wiki/Large-scale_structure_of_the_universe" class="mw-redirect" title="Large-scale structure of the universe">large-scale structure of the universe</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Dark_energy">Dark energy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=16" title="Edit section: Dark energy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Dark_energy" title="Dark energy">Dark energy</a></div> <p>Around 3 billion years ago, at a time of about 11 billion years, dark energy is believed to have begun to dominate the energy density of the universe. This transition came about because dark energy does not dilute as the universe expands, instead maintaining a constant energy density. Similarly to inflation, dark energy drives accelerated expansion, such that the scale factor grows exponentially in time. </p> <div class="mw-heading mw-heading2"><h2 id="Measuring_the_expansion_rate">Measuring the expansion rate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=17" title="Edit section: Measuring the expansion rate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Redshift_blueshift.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Redshift_blueshift.svg/260px-Redshift_blueshift.svg.png" decoding="async" width="260" height="163" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Redshift_blueshift.svg/390px-Redshift_blueshift.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Redshift_blueshift.svg/520px-Redshift_blueshift.svg.png 2x" data-file-width="800" data-file-height="500" /></a><figcaption>When an object is receding, its light gets stretched (redshifted). When the object is approaching, its light gets compressed (<a href="/wiki/Blueshift" class="mw-redirect" title="Blueshift">blueshifted</a>).</figcaption></figure> <p>The most direct way to measure the expansion rate is to independently measure the recession velocities and the distances of distant objects, such as galaxies. The ratio between these quantities gives the Hubble rate, in accordance with Hubble's law. Typically, the distance is measured using a <a href="/wiki/Cosmic_distance_ladder" title="Cosmic distance ladder">standard candle</a>, which is an object or event for which the <a href="/wiki/Intrinsic_brightness" class="mw-redirect" title="Intrinsic brightness">intrinsic brightness</a> is known. The object's distance can then be inferred from the observed <a href="/wiki/Apparent_brightness" class="mw-redirect" title="Apparent brightness">apparent brightness</a>. Meanwhile, the recession speed is measured through the redshift. Hubble used this approach for his original measurement of the expansion rate, by measuring the brightness of <a href="/wiki/Cepheid_variable_stars" class="mw-redirect" title="Cepheid variable stars">Cepheid variable stars</a> and the redshifts of their host galaxies. More recently, using <a href="/wiki/Type_Ia_supernovae" class="mw-redirect" title="Type Ia supernovae">Type Ia supernovae</a>, the expansion rate was measured to be <i>H</i><sub>0</sub><span class="nowrap"> </span>=<span class="nowrap"> </span><span class="nowrap"><span data-sort-value="7001732400000000000♠"></span>73.24<span style="margin-left:0.3em;margin-right:0.15em;">±</span>1.74 (km/s)/Mpc</span>.<sup id="cite_ref-Riess2016_22-0" class="reference"><a href="#cite_note-Riess2016-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> This means that for every million <a href="/wiki/Parsec" title="Parsec">parsecs</a> of distance from the observer, recessional velocity of objects at that distance increases by about 73 kilometres per second (160,000 mph). </p><p>Supernovae are observable at such great distances that the light travel time therefrom can approach the age of the universe. Consequently, they can be used to measure not only the present-day expansion rate but also the expansion history. In work that was awarded the 2011 <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a>, supernova observations were used to determine that cosmic expansion is accelerating in the present epoch.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>By assuming a cosmological model, e.g. the <a href="/wiki/Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a>, another possibility is to infer the present-day expansion rate from the sizes of the largest fluctuations seen in the <a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a>. A higher expansion rate would imply a smaller characteristic size of CMB fluctuations, and vice versa. The <a href="/wiki/Planck_(spacecraft)" title="Planck (spacecraft)">Planck collaboration</a> measured the expansion rate this way and determined <i>H</i><sub>0</sub> = <span class="nowrap"><span data-sort-value="7001674000000000000♠"></span>67.4<span style="margin-left:0.3em;margin-right:0.15em;">±</span>0.5 (km/s)/Mpc</span>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> There is a disagreement between this measurement and the supernova-based measurements, known as the <a href="/wiki/Hubble_tension" class="mw-redirect" title="Hubble tension">Hubble tension</a>. </p><p>A third option proposed recently is to use information from <a href="/wiki/Gravitational_wave" title="Gravitational wave">gravitational wave</a> events (especially those involving the <a href="/wiki/Neutron_star_merger" title="Neutron star merger">merger of neutron stars</a>, like <a href="/wiki/GW170817" title="GW170817">GW170817</a>), to measure the expansion rate.<sup id="cite_ref-PHYS-20181022_25-0" class="reference"><a href="#cite_note-PHYS-20181022-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-NAT-20181017_26-0" class="reference"><a href="#cite_note-NAT-20181017-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Such measurements do not yet have the precision to resolve the Hubble tension. </p><p>In principle, the cosmic expansion history can also be measured by studying how redshifts, distances, fluxes, angular positions, and angular sizes of astronomical objects change over the course of the time that they are being observed. These effects are too small to have yet been detected. However, changes in redshift or flux could be observed by the <a href="/wiki/Square_Kilometre_Array" title="Square Kilometre Array">Square Kilometre Array</a> or <a href="/wiki/Extremely_Large_Telescope" title="Extremely Large Telescope">Extremely Large Telescope</a> in the mid-2030s.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Conceptual_considerations_and_misconceptions">Conceptual considerations and misconceptions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=18" title="Edit section: Conceptual considerations and misconceptions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Measuring_distances_in_expanding_space">Measuring distances in expanding space</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=19" title="Edit section: Measuring distances in expanding space"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output 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class="mbox-text-span">This section <b>is written like a <a href="/wiki/Wikipedia:What_Wikipedia_is_not#Wikipedia_is_not_a_publisher_of_original_thought" title="Wikipedia:What Wikipedia is not">personal reflection, personal essay, or argumentative essay</a></b> that states a Wikipedia editor's personal feelings or presents an original argument about a topic.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Expansion_of_the_universe&action=edit">help improve it</a> by rewriting it in an <a href="/wiki/Wikipedia:Writing_better_articles#Information_style_and_tone" title="Wikipedia:Writing better articles">encyclopedic style</a>.</span> <span class="date-container"><i>(<span class="date">August 2015</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this 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Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Expansion+of+the+universe%22">"Expansion of the universe"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Expansion+of+the+universe%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Expansion+of+the+universe%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Expansion+of+the+universe%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Expansion+of+the+universe%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Expansion+of+the+universe%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">May 2021</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti 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img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:254px;max-width:254px"><div class="trow"><div class="tsingle" style="width:252px;max-width:252px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Embedded_LambdaCDM_geometry.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Embedded_LambdaCDM_geometry.png/250px-Embedded_LambdaCDM_geometry.png" decoding="async" width="250" height="213" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Embedded_LambdaCDM_geometry.png/375px-Embedded_LambdaCDM_geometry.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Embedded_LambdaCDM_geometry.png/500px-Embedded_LambdaCDM_geometry.png 2x" data-file-width="640" data-file-height="544" /></a></span></div></div></div><div class="trow"><div class="tsingle" style="width:252px;max-width:252px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Embedded_LambdaCDM_geometry_(alt_view).png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Embedded_LambdaCDM_geometry_%28alt_view%29.png/250px-Embedded_LambdaCDM_geometry_%28alt_view%29.png" decoding="async" width="250" height="244" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Embedded_LambdaCDM_geometry_%28alt_view%29.png/375px-Embedded_LambdaCDM_geometry_%28alt_view%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Embedded_LambdaCDM_geometry_%28alt_view%29.png/500px-Embedded_LambdaCDM_geometry_%28alt_view%29.png 2x" data-file-width="640" data-file-height="624" /></a></span></div><div class="thumbcaption">Two views of an <a href="/wiki/Isometric_embedding" class="mw-redirect" title="Isometric embedding">isometric embedding</a> of part of the <a href="/wiki/Visible_universe" class="mw-redirect" title="Visible universe">visible universe</a> over most of its history, showing how a light ray (red line) can travel an effective distance of 28 billion <a href="/wiki/Light_year" class="mw-redirect" title="Light year">light years</a> (orange line) in just 13.8 billion years of <a href="/wiki/Cosmological_time" class="mw-redirect" title="Cosmological time">cosmological time</a>. (<a href="/wiki/File:Embedded_LambdaCDM_geometry.png#Mathematical_details" title="File:Embedded LambdaCDM geometry.png">Mathematical details</a>)</div></div></div></div></div> <p>At cosmological scales, the present universe conforms to <a href="/wiki/Euclidean_space" title="Euclidean space">Euclidean space</a>, what cosmologists describe as <i>geometrically flat</i>, to within experimental error.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>Consequently, the rules of <a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a> associated with <a href="/wiki/Parallel_postulate" title="Parallel postulate">Euclid's fifth postulate</a> hold in the present universe in 3D space. It is, however, possible that the geometry of past 3D space could have been highly curved. The curvature of space is often modeled using a non-zero <a href="/wiki/Riemann_curvature_tensor" title="Riemann curvature tensor">Riemann curvature tensor</a> in <a href="/wiki/Curvature_of_Riemannian_manifolds" title="Curvature of Riemannian manifolds">curvature of Riemannian manifolds</a>. Euclidean "geometrically flat" space has a Riemann curvature tensor of zero. </p><p>"Geometrically flat" space has three dimensions and is consistent with Euclidean space. However, <a href="/wiki/Spacetime" title="Spacetime">spacetime</a> has four dimensions; it is not flat according to Einstein's general theory of relativity. Einstein's theory postulates that "matter and energy curve spacetime, and there is enough matter and energy to provide for curvature."<sup id="cite_ref-Sc-am-11_29-0" class="reference"><a href="#cite_note-Sc-am-11-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p><p>In part to accommodate such different geometries, the expansion of the universe is inherently general-relativistic. It cannot be modeled with <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> alone: Though <a href="/wiki/Milne_universe" class="mw-redirect" title="Milne universe">such models</a> exist, they may be at fundamental odds with the observed interaction between matter and spacetime seen in the universe. </p><p>The images to the right show two views of <a href="/wiki/Spacetime_diagram" title="Spacetime diagram">spacetime diagrams</a> that show the large-scale geometry of the universe according to the <a href="/wiki/%CE%9BCDM" class="mw-redirect" title="ΛCDM">ΛCDM</a> cosmological model. Two of the dimensions of space are omitted, leaving one dimension of space (the dimension that grows as the cone gets larger) and one of time (the dimension that proceeds "up" the cone's surface). The narrow circular end of the diagram corresponds to a <a href="/wiki/Cosmological_time" class="mw-redirect" title="Cosmological time">cosmological time</a> of 700 million years after the Big Bang, while the wide end is a cosmological time of 18 billion years, where one can see the beginning of the <a href="/wiki/Accelerating_universe" class="mw-redirect" title="Accelerating universe">accelerating expansion</a> as a splaying outward of the spacetime, a feature that eventually dominates in this model. The purple grid lines mark cosmological time at intervals of one billion years from the Big Bang. The cyan grid lines mark <a href="/wiki/Comoving_distance" class="mw-redirect" title="Comoving distance">comoving distance</a> at intervals of one billion light-years in the present era (less in the past and more in the future). The circular curling of the surface is an artifact of the embedding with no physical significance and is done for illustrative purposes; a flat universe does not curl back onto itself. (A similar effect can be seen in the tubular shape of the <a href="/wiki/Pseudosphere" title="Pseudosphere">pseudosphere</a>.) </p><p>The brown line on the diagram is the <a href="/wiki/Worldline" class="mw-redirect" title="Worldline">worldline</a> of Earth (or more precisely its location in space, even before it was formed). The yellow line is the worldline of the most distant known <a href="/wiki/Quasar" title="Quasar">quasar</a>. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching Earth at the present day. The orange line shows the present-day distance between the quasar and Earth, about 28 billion light-years, which is a larger distance than the age of the universe multiplied by the speed of light, <i>ct</i>. </p><p>According to the <a href="/wiki/Equivalence_principle" title="Equivalence principle">equivalence principle</a> of general relativity, the rules of special relativity are <i>locally</i> valid in small regions of spacetime that are approximately flat. In particular, light always travels locally at the speed <i>c</i>; in the diagram, this means, according to the convention of constructing spacetime diagrams, that light beams always make an angle of 45° with the local grid lines. It does not follow, however, that light travels a distance <i>ct</i> in a time <i>t</i>, as the red worldline illustrates. While it always moves locally at <i>c</i>, its time in transit (about 13 billion years) is not related to the distance traveled in any simple way, since the universe expands as the light beam traverses space and time. The distance traveled is thus inherently ambiguous because of the changing scale of the universe. Nevertheless, there are two distances that appear to be physically meaningful: the distance between Earth and the quasar when the light was emitted, and the distance between them in the present era (taking a slice of the cone along the dimension defined as the spatial dimension). The former distance is about 4 billion light-years, much smaller than <i>ct</i>, whereas the latter distance (shown by the orange line) is about 28 billion light-years, much larger than <i>ct</i>. In other words, if space were not expanding today, it would take 28 billion years for light to travel between Earth and the quasar, while if the expansion had stopped at the earlier time, it would have taken only 4 billion years. </p><p>The light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light-years away. In fact, the light emitted towards Earth was actually moving <i>away</i> from Earth when it was first emitted; the metric distance to Earth increased with cosmological time for the first few billion years of its travel time, also indicating that the expansion of space between Earth and the quasar at the early time was faster than the speed of light. None of this behavior originates from a special property of metric expansion, but rather from local principles of special relativity <a href="/wiki/Integral" title="Integral">integrated</a> over a curved surface. </p> <div class="mw-heading mw-heading3"><h3 id="Topology_of_expanding_space">Topology of expanding space</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=20" title="Edit section: Topology of expanding space"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Over time, the <a href="/wiki/Space" title="Space">space</a> that makes up the <a href="/wiki/Universe" title="Universe">universe</a> is expanding. The words '<a href="/wiki/Space" title="Space">space</a>' and '<a href="/wiki/Universe" title="Universe">universe</a>', sometimes used interchangeably, have distinct meanings in this context. Here 'space' is a mathematical concept that stands for the three-dimensional <a href="/wiki/Manifold" title="Manifold">manifold</a> into which our respective positions are embedded, while 'universe' refers to everything that exists, including the matter and energy in space, the extra dimensions that may be wrapped up in <a href="/wiki/String_theory" title="String theory">various strings</a>, and the time through which various events take place. The expansion of space is in reference to this 3D manifold only; that is, the description involves no structures such as extra dimensions or an exterior universe.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>The ultimate <a href="/wiki/Topology" title="Topology">topology</a> of space is <i><a href="/wiki/A_priori_and_a_posteriori" title="A priori and a posteriori">a posteriori</a></i> – something that in principle must be observed – as there are no constraints that can simply be reasoned out (in other words there cannot be any <i><a href="/wiki/A_priori_and_a_posteriori" title="A priori and a posteriori">a priori</a></i> constraints) on how the space in which we live is <a href="/wiki/Simply_connected_space" title="Simply connected space">connected</a> or whether it wraps around on itself as a <a href="/wiki/Compact_space" title="Compact space">compact space</a>. Though certain cosmological models such as <a href="/wiki/G%C3%B6del_metric" title="Gödel metric">Gödel's universe</a> even permit bizarre <a href="/wiki/Worldline" class="mw-redirect" title="Worldline">worldlines</a> that intersect with themselves, ultimately the question as to whether we are in something like a "<a href="/wiki/Pac-Man" title="Pac-Man">Pac-Man</a> universe", where if traveling far enough in one direction would allow one to simply end up back in the same place like going all the way around the surface of a balloon (or a planet like the Earth), is <a href="/wiki/Shape_of_the_universe#Detection" title="Shape of the universe">an observational question that is constrained as measurable or non-measurable by the universe's global geometry</a>. At present, observations are consistent with the universe having infinite extent and being a <a href="/wiki/Simply_connected_space" title="Simply connected space">simply connected space</a>, though <a href="/wiki/Cosmological_horizon" title="Cosmological horizon">cosmological horizons</a> limit our ability to distinguish between simple and more complicated proposals. The universe could be infinite in extent or it could be finite; but the evidence that leads to the <a href="/wiki/Cosmic_inflation" title="Cosmic inflation">inflationary model</a> of the early universe also implies that the "total universe" is much larger than the observable universe. Thus any edges or exotic geometries or topologies would not be directly observable, since light has not reached scales on which such aspects of the universe, if they exist, are still allowed. For all intents and purposes, it is safe to assume that the universe is infinite in spatial extent, without edge or strange connectedness.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p><p>Regardless of the overall shape of the universe, the question of what the universe is expanding into is one that does not require an answer, according to the theories that describe the expansion; the way we define space in our universe in no way requires additional exterior space into which it can expand, since an expansion of an infinite expanse can happen without changing the infinite extent of the expanse. All that is certain is that the manifold of space in which we live simply has the property that the distances between objects are getting larger as time goes on. This only implies the simple observational consequences associated with the metric expansion explored below. No "outside" or embedding in hyperspace is required for an expansion to occur. The visualizations often seen of the universe growing as a bubble into nothingness are misleading in that respect. There is no reason to believe there is anything "outside" the expanding universe into which the universe expands. </p><p>Even if the overall spatial extent is infinite and thus the universe cannot get any "larger", we still say that space is expanding because, locally, the characteristic distance between objects is increasing. As an infinite space grows, it remains infinite. </p> <div class="mw-heading mw-heading3"><h3 id="Density_of_universe_during_expansion">Density of universe during expansion</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=21" title="Edit section: Density of universe during expansion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Despite being extremely <a href="/wiki/Density" title="Density">dense</a> when very young and during part of its early expansion – far denser than is usually required to form a <a href="/wiki/Black_hole" title="Black hole">black hole</a> – the universe did not re-collapse into a black hole. This is because commonly used calculations for <a href="/wiki/Gravitational_collapse" title="Gravitational collapse">gravitational collapse</a> are usually based upon objects of relatively constant size, such as <a href="/wiki/Star" title="Star">stars</a>, and do not apply to rapidly expanding space such as the Big Bang.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (April 2024)">citation needed</span></a></i>]</sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Accuracy_dispute#Disputed_statement" title="Wikipedia:Accuracy dispute"><span title="The material near this tag is possibly inaccurate or nonfactual. (April 2024)">dubious</span></a> – <a href="/wiki/Talk:Expansion_of_the_universe#Density_of_universe_during_expansion" title="Talk:Expansion of the universe">discuss</a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Effects_of_expansion_on_small_scales">Effects of expansion on small scales</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=22" title="Edit section: Effects of expansion on small scales"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The expansion of space is sometimes described as a force that acts to push objects apart. Though this is an accurate description of the effect of the cosmological constant, it is not an accurate picture of the phenomenon of expansion in general.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Raisinbread.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Raisinbread.gif/260px-Raisinbread.gif" decoding="async" width="260" height="221" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Raisinbread.gif/390px-Raisinbread.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Raisinbread.gif/520px-Raisinbread.gif 2x" data-file-width="735" data-file-height="625" /></a><figcaption>Animation of an expanding raisin-bread model. As the bread doubles in width (depth and length), the distances between raisins also double.</figcaption></figure> <p>In addition to slowing the overall expansion, gravity causes local clumping of matter into stars and galaxies. Once objects are formed and bound by gravity, they "drop out" of the expansion and do not subsequently expand under the influence of the cosmological metric, there being no force compelling them to do so. </p><p>There is no difference between the inertial expansion of the universe and the inertial separation of nearby objects in a vacuum; the former is simply a large-scale extrapolation of the latter. </p><p>Once objects are bound by gravity, they no longer recede from each other. Thus, the <a href="/wiki/Andromeda_Galaxy" title="Andromeda Galaxy">Andromeda Galaxy</a>, which is bound to the <a href="/wiki/Milky_Way" title="Milky Way">Milky Way Galaxy</a>, is actually falling <i>towards</i> us and is not expanding away. Within the <a href="/wiki/Local_Group" title="Local Group">Local Group</a>, the gravitational interactions have changed the inertial patterns of objects such that there is no cosmological expansion taking place. Beyond the Local Group, the inertial expansion is measurable, though systematic gravitational effects imply that larger and larger parts of space will eventually fall out of the "<a href="/wiki/Hubble_Flow" class="mw-redirect" title="Hubble Flow">Hubble Flow</a>" and end up as bound, non-expanding objects up to the scales of <a href="/wiki/Supercluster" title="Supercluster">superclusters</a> of galaxies. Such future events are predicted by knowing the precise way the Hubble Flow is changing as well as the masses of the objects to which we are being gravitationally pulled. Currently, the Local Group is being gravitationally pulled towards either the <a href="/wiki/Shapley_Supercluster" title="Shapley Supercluster">Shapley Supercluster</a> or the "<a href="/wiki/Great_Attractor" title="Great Attractor">Great Attractor</a>", with which we would eventually merge if dark energy were not acting. </p><p>A consequence of metric expansion being due to inertial motion is that a uniform local "explosion" of matter into a vacuum can be locally described by the <a href="/wiki/FLRW_metric" class="mw-redirect" title="FLRW metric">FLRW geometry</a>, the same geometry that describes the expansion of the universe as a whole and was also the basis for the simpler <a href="/wiki/Milne_universe" class="mw-redirect" title="Milne universe">Milne universe</a>, which ignores the effects of gravity. In particular, general relativity predicts that light will move at the speed <i>c</i> with respect to the local motion of the exploding matter, a phenomenon analogous to <a href="/wiki/Frame_dragging" class="mw-redirect" title="Frame dragging">frame dragging</a>. </p><p>The situation changes somewhat with the introduction of dark energy or a cosmological constant. A cosmological constant due to a <a href="/wiki/Vacuum_energy" title="Vacuum energy">vacuum energy</a> density has the effect of adding a repulsive force between objects that is proportional (not inversely proportional) to distance. Unlike inertia it actively "pulls" on objects that have clumped together under the influence of gravity, and even on individual atoms. However, this does not cause the objects to grow steadily or to disintegrate; unless they are very weakly bound, they will simply settle into an equilibrium state that is slightly (undetectably) larger than it would otherwise have been. As the universe expands and the matter in it thins, the gravitational attraction decreases (since it is proportional to the density), while the cosmological repulsion increases. Thus, the ultimate fate of the ΛCDM universe is a near-vacuum expanding at an ever-increasing rate under the influence of the cosmological constant. However, gravitationally bound objects like the Milky Way do not expand, and the Andromeda Galaxy is moving fast enough towards us that it will still merge with the Milky Way in around 3 billion years. </p> <div class="mw-heading mw-heading3"><h3 id="Metric_expansion_and_speed_of_light">Metric expansion and speed of light</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=23" title="Edit section: Metric expansion and speed of light"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At the end of the <a href="/wiki/Early_universe" class="mw-redirect" title="Early universe">early universe</a>'s inflationary period, all the matter and energy in the universe was set on an <a href="/wiki/Inertia" title="Inertia">inertial trajectory</a> consistent with the <a href="/wiki/Equivalence_principle" title="Equivalence principle">equivalence principle</a> and <a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein's</a> <a href="/wiki/General_theory_of_relativity" class="mw-redirect" title="General theory of relativity">general theory of relativity</a>. This is when the <a href="/wiki/Hubble%27s_law" title="Hubble's law">precise and regular form of the universe's expansion</a> had its origin (that is, matter in the universe is separating because it was separating in the past due to the <a href="/wiki/Inflaton_field" class="mw-redirect" title="Inflaton field">inflaton field</a>).<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="this seems original research, the causes for inflation are still debated, the same for possible pre-inflation non-homogeneity of the universe (August 2015)">citation needed</span></a></i>]</sup> </p><p>While special relativity prohibits objects from moving faster than light with respect to a <a href="/wiki/Local_reference_frame" title="Local reference frame">local reference frame</a> where spacetime can be treated as <a href="/wiki/Minkowski_space" title="Minkowski space">flat and unchanging</a>, it does not apply to situations where <a href="/wiki/Spacetime_curvature" class="mw-redirect" title="Spacetime curvature">spacetime curvature</a> or evolution in time become important. These situations are described by general relativity, which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "distance" here is somewhat different from that used in an inertial frame. The definition of distance used here is the summation or integration of local <a href="/wiki/Comoving_distance" class="mw-redirect" title="Comoving distance">comoving distances</a>, all done at constant local proper time. For example, galaxies that are farther than the <a href="/wiki/Hubble_radius" class="mw-redirect" title="Hubble radius">Hubble radius</a>, approximately 4.5 <a href="/wiki/Gigaparsec" class="mw-redirect" title="Gigaparsec">gigaparsecs</a> or 14.7 billion <a href="/wiki/Light-year" title="Light-year">light-years</a>, away from us have a recession speed that is faster than the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>. Visibility of these objects depends on the exact expansion history of the universe. Light that is emitted today from galaxies beyond the more-distant <a href="/wiki/Cosmological_horizon#Event_horizon" title="Cosmological horizon">cosmological event horizon</a>, about 5 gigaparsecs or 16 billion light-years, will never reach us, although we can still see the light that these galaxies emitted in the past. Because of the high rate of expansion, it is also possible for a distance between two objects to be greater than the value calculated by multiplying the speed of light by the age of the universe. These details are a frequent source of confusion among amateurs and even professional physicists.<sup id="cite_ref-astro-ph/0310808_33-0" class="reference"><a href="#cite_note-astro-ph/0310808-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> Due to the non-intuitive nature of the subject and what has been described by some as "careless" choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion within the fields of education and communication of scientific concepts.<sup id="cite_ref-Whiting_34-0" class="reference"><a href="#cite_note-Whiting-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Hogg_35-0" class="reference"><a href="#cite_note-Hogg-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Baryshev_36-0" class="reference"><a href="#cite_note-Baryshev-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Peacock_37-0" class="reference"><a href="#cite_note-Peacock-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Common_analogies_for_cosmic_expansion">Common analogies for cosmic expansion</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=24" title="Edit section: Common analogies for cosmic expansion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The expansion of the universe is often illustrated with conceptual models where an expanding object is taken to represent expanding space. These models can be misleading to the extent that they give the false impression that expanding space must carry objects with it. In reality, the expansion of the universe can alternatively be thought of as corresponding only to the inertial motion of objects away from one another. </p><p>In the "<a href="/wiki/Ant_on_a_rubber_rope" title="Ant on a rubber rope">ant on a rubber rope</a> model" one imagines an ant (idealized as pointlike) crawling at a constant speed on a perfectly elastic rope that is constantly stretching. If we stretch the rope in accordance with the ΛCDM scale factor and think of the ant's speed as the speed of light, then this analogy is conceptually accurate – the ant's position over time will match the path of the red line on the embedding diagram above. </p><p>In the "rubber sheet model", one replaces the rope with a flat two-dimensional rubber sheet that expands uniformly in all directions. The addition of a second spatial dimension allows for the possibility of showing local perturbations of the spatial geometry by local curvature in the sheet. </p><p>In the "balloon model" the flat sheet is replaced by a spherical balloon that is inflated from an initial size of zero (representing the Big Bang). A balloon has positive <a href="/wiki/Gaussian_curvature" title="Gaussian curvature">Gaussian curvature</a>, even though observations suggest that the real universe is spatially flat, but this inconsistency can be eliminated by making the balloon very large so that it is locally flat within the limits of observation. This analogy is potentially confusing since it could wrongly suggest that the Big Bang took place at the center of the balloon. In fact points off the surface of the balloon have no meaning, even if they were occupied by the balloon at an earlier time or will be occupied later. </p><p>In the "raisin bread model", one imagines a loaf of raisin bread expanding in an oven. The loaf (space) expands as a whole, but the raisins (gravitationally bound objects) do not expand; they merely move farther away from each other. This analogy has the disadvantage of wrongly implying that the expansion has a center and an edge. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=25" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Comoving_and_proper_distances" title="Comoving and proper distances">Comoving and proper distances</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=26" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-NYT-20170220-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-NYT-20170220_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFOverbye2017" class="citation news cs1"><a href="/wiki/Dennis_Overbye" title="Dennis Overbye">Overbye, Dennis</a> (20 February 2017). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2017/02/20/science/hubble-constant-universe-expanding-speed.html">"Cosmos Controversy: The Universe Is Expanding, but How Fast?"</a>. <i><a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a></i><span class="reference-accessdate">. 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"Expanding Space: The Root of Conceptual Problems of the Cosmological Physics". <i>Practical Cosmology</i>. <b>2</b>: 20–30. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0810.0153">0810.0153</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008pc2..conf...20B">2008pc2..conf...20B</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Practical+Cosmology&rft.atitle=Expanding+Space%3A+The+Root+of+Conceptual+Problems+of+the+Cosmological+Physics&rft.volume=2&rft.pages=20-30&rft.date=2008&rft_id=info%3Aarxiv%2F0810.0153&rft_id=info%3Abibcode%2F2008pc2..conf...20B&rft.aulast=Baryshev&rft.aufirst=Yu.+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AExpansion+of+the+universe" class="Z3988"></span></span> </li> <li id="cite_note-Peacock-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-Peacock_37-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeacock2008" class="citation arxiv cs1">Peacock, J. 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"A diatribe on expanding space". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0809.4573">0809.4573</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/astro-ph">astro-ph</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=A+diatribe+on+expanding+space&rft.date=2008&rft_id=info%3Aarxiv%2F0809.4573&rft.aulast=Peacock&rft.aufirst=J.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AExpansion+of+the+universe" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Printed_references">Printed references</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=27" title="Edit section: Printed references"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Eddington, Arthur. <i>The Expanding Universe: Astronomy's 'Great Debate', 1900–1931</i>. Press Syndicate of the University of Cambridge, 1933.</li> <li>Liddle, Andrew R. and Lyth, David H. <i>Cosmological Inflation and Large-Scale Structure</i>. Cambridge University Press, 2000.</li> <li>Lineweaver, Charles H. and Davis, Tamara M. "<a rel="nofollow" class="external text" href="http://www.scientificamerican.com/article/misconceptions-about-the-2005-03/">Misconceptions about the Big Bang</a>", <i><a href="/wiki/Scientific_American" title="Scientific American">Scientific American</a></i>, March 2005 (non-free content).</li> <li>Mook, Delo E. and <a href="/wiki/Thomas_Vargish" title="Thomas Vargish">Thomas Vargish</a>. <i>Inside Relativity</i>. Princeton University Press, 1991.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Expansion_of_the_universe&action=edit&section=28" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output 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typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Expansion_of_the_universe" class="extiw" title="commons:Category:Expansion of the universe">Expansion of the universe</a></span>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Expansion_of_the_universe" class="extiw" title="q:Special:Search/Expansion of the universe">Expansion of the universe</a></b></i>.</div></div> </div> <ul><li>Swenson, Jim, <a rel="nofollow" class="external text" href="http://www.newton.dep.anl.gov/askasci/phy00/phy00812.htm">Answer to a question about the expanding universe</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090111084313/http://www.newton.dep.anl.gov/askasci/phy00/phy00812.htm">Archived</a> 11 January 2009 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li>Felder, Gary, "<a rel="nofollow" class="external text" href="http://www.felderbooks.com/papers/cosmo.html">The Expanding universe</a>".</li> <li><a href="/wiki/NASA" title="NASA">NASA</a>'s <a href="/wiki/WMAP" class="mw-redirect" title="WMAP">WMAP</a> team offers an "<a rel="nofollow" class="external text" href="https://map.gsfc.nasa.gov/m_uni/uni_101bbtest1.html">Explanation of the universal expansion</a>" at an elementary level.</li> <li><a rel="nofollow" class="external text" href="http://cmb.physics.wisc.edu/pub/tutorial/hubble.html">Hubble Tutorial from the University of Wisconsin Physics Department</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140609025301/http://cmb.physics.wisc.edu/pub/tutorial/hubble.html">Archived</a> 9 June 2014 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130922085443/http://theory.uwinnipeg.ca/mod_tech/node216.html">Expanding raisin bread</a> from the University of Winnipeg: an illustration, but no explanation</li> <li><a rel="nofollow" class="external text" href="http://www.ucolick.org/~mountain/AAA/aaa_old/030209.html#expansion">"Ant on a balloon" analogy to explain the expanding universe</a> at "Ask an Astronomer" (the astronomer who provides this explanation is not specified).</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output 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.mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Cosmology" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Cosmology_topics" title="Template:Cosmology topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Cosmology_topics" title="Template talk:Cosmology topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Cosmology_topics" title="Special:EditPage/Template:Cosmology topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Cosmology" style="font-size:114%;margin:0 4em"><a href="/wiki/Cosmology" title="Cosmology">Cosmology</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Age_of_the_universe" title="Age of the universe">Age of the universe</a></li> <li><a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a></li> <li><a href="/wiki/Chronology_of_the_universe" title="Chronology of the universe">Chronology of the universe</a></li> <li><a href="/wiki/Universe" title="Universe">Universe</a></li> <li><a href="/wiki/Observable_universe" title="Observable universe">Observable universe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">History of<br />cosmological theories</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discovery_of_cosmic_microwave_background_radiation" title="Discovery of cosmic microwave background radiation">Discovery of cosmic microwave background</a></li> <li><a href="/wiki/History_of_the_Big_Bang_theory" title="History of the Big Bang theory">History of the Big Bang theory</a></li> <li><a href="/wiki/Religious_interpretations_of_the_Big_Bang_theory" title="Religious interpretations of the Big Bang theory">Religious interpretations of the Big Bang</a></li> <li><a href="/wiki/Timeline_of_cosmological_theories" title="Timeline of cosmological theories">Timeline of cosmological theories</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Past universe</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">Cosmic microwave background</a></li> <li><a href="/wiki/Cosmic_neutrino_background" title="Cosmic neutrino background">Cosmic neutrino background</a></li> <li><a href="/wiki/Gravitational_wave_background" title="Gravitational wave background">Gravitational wave background</a></li> <li><a href="/wiki/Inflation_(cosmology)" class="mw-redirect" title="Inflation (cosmology)">Inflation</a></li> <li><a href="/wiki/Big_Bang_nucleosynthesis" title="Big Bang nucleosynthesis">Nucleosynthesis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Present universe</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">FLRW metric</a></li> <li><a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann equations</a></li> <li><a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a></li> <li><a class="mw-selflink selflink">Expansion of the universe</a></li> <li><a href="/wiki/Accelerating_expansion_of_the_universe" title="Accelerating expansion of the universe">Accelerating expansion</a></li> <li><a href="/wiki/Redshift" title="Redshift">Redshift</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Future universe</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Future_of_an_expanding_universe" title="Future of an expanding universe">Future of an expanding universe</a></li> <li><a href="/wiki/Ultimate_fate_of_the_universe" title="Ultimate fate of the universe">Ultimate fate of the universe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Components</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dark_energy" title="Dark energy">Dark energy</a></li> <li><a href="/wiki/Dark_fluid" title="Dark fluid">Dark fluid</a></li> <li><a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li> <li><a href="/wiki/Quintessence_(physics)" title="Quintessence (physics)">Quintessence</a></li> <li><a href="/wiki/Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Structure formation</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Galaxy_filament" title="Galaxy filament">Galaxy filament</a></li> <li><a href="/wiki/Galaxy_formation_and_evolution" title="Galaxy formation and evolution">Galaxy formation</a></li> <li><a href="/wiki/Large_quasar_group" title="Large quasar group">Large quasar group</a></li> <li><a href="/wiki/Large-scale_structure_of_the_cosmos" class="mw-redirect" title="Large-scale structure of the cosmos">Large-scale structure</a></li> <li><a href="/wiki/Reionization" title="Reionization">Reionization</a></li> <li><a href="/wiki/Shape_of_the_universe" title="Shape of the universe">Shape of the universe</a></li> <li><a href="/wiki/Structure_formation" title="Structure formation">Structure formation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Experiments</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a 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