CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="ja" dir="ltr"> <head> <meta charset="UTF-8"> <title>スケール因子 (宇宙論) - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )jawikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"ja", "wgMonthNames":["","1月","2月","3月","4月","5月","6月","7月","8月","9月","10月","11月","12月"],"wgRequestId":"a62e7606-8ebc-4739-83b5-69ed447d1d3f","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"スケール因子_(宇宙論)","wgTitle":"スケール因子 (宇宙論)","wgCurRevisionId":101661688,"wgRevisionId":101661688,"wgArticleId":3018343,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Webarchiveテンプレートのウェイバックリンク","日本語版記事がリダイレクトの仮リンクを含む記事","すべてのスタブ記事","物理学関連のスタブ項目","数学関連のスタブ項目","宇宙論","数学に関する記事"],"wgPageViewLanguage":"ja","wgPageContentLanguage":"ja","wgPageContentModel":"wikitext","wgRelevantPageName":"スケール因子_(宇宙論)","wgRelevantArticleId":3018343,"wgIsProbablyEditable":true, "wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"ja","pageLanguageDir":"ltr","pageVariantFallbacks":"ja"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":6000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q1332997","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled": false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.gadget.PDFLinkIcon":"ready","ext.gadget.RedirectColor":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.NormalizeCharWidth","ext.gadget.suppressEnterAtSummaryBox","ext.gadget.checkSignature","ext.gadget.charinsert","ext.gadget.WikiMiniAtlas","ext.gadget.switcher","ext.gadget.protectionIndicator", "ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.quicksurveys.init","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=ja&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=ja&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=ja&modules=ext.gadget.PDFLinkIcon%2CRedirectColor&only=styles&skin=vector-2022"> <link rel="stylesheet" href="/w/load.php?lang=ja&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.6"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="スケール因子 (宇宙論) - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//ja.m.wikipedia.org/wiki/%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)"> <link rel="alternate" type="application/x-wiki" title="編集" href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (ja)"> <link rel="EditURI" type="application/rsd+xml" href="//ja.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://ja.wikipedia.org/wiki/%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.ja"> <link rel="alternate" type="application/atom+xml" title="WikipediaのAtomフィード" href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E6%9C%80%E8%BF%91%E3%81%AE%E6%9B%B4%E6%96%B0&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-スケール因子_宇宙論 rootpage-スケール因子_宇宙論 skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">コンテンツにスキップ</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="サイト"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="メインメニュー" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">メインメニュー</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">メインメニュー</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">非表示</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> 案内 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/%E3%83%A1%E3%82%A4%E3%83%B3%E3%83%9A%E3%83%BC%E3%82%B8" title="メインページに移動する [z]" accesskey="z"><span>メインページ</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:%E3%82%B3%E3%83%9F%E3%83%A5%E3%83%8B%E3%83%86%E3%82%A3%E3%83%BB%E3%83%9D%E3%83%BC%E3%82%BF%E3%83%AB" title="このプロジェクトについて、できること、情報を入手する場所"><span>コミュニティ・ポータル</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:%E6%9C%80%E8%BF%91%E3%81%AE%E5%87%BA%E6%9D%A5%E4%BA%8B" title="最近の出来事の背景を知る"><span>最近の出来事</span></a></li><li id="n-newpages" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E6%96%B0%E3%81%97%E3%81%84%E3%83%9A%E3%83%BC%E3%82%B8" title="最近新規に作成されたページの一覧"><span>新しいページ</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E6%9C%80%E8%BF%91%E3%81%AE%E6%9B%B4%E6%96%B0" title="このウィキにおける最近の更新の一覧 [r]" accesskey="r"><span>最近の更新</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E3%81%8A%E3%81%BE%E3%81%8B%E3%81%9B%E8%A1%A8%E7%A4%BA" title="無作為に選択されたページを読み込む [x]" accesskey="x"><span>おまかせ表示</span></a></li><li id="n-sandbox" class="mw-list-item"><a href="/wiki/Wikipedia:%E3%82%B5%E3%83%B3%E3%83%89%E3%83%9C%E3%83%83%E3%82%AF%E3%82%B9" title="練習用のページ"><span>練習用ページ</span></a></li><li id="n-commonsupload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=ja" title="画像やメディアファイルをウィキメディア・コモンズにアップロード"><span>アップロード (ウィキメディア・コモンズ)</span></a></li> </ul> </div> </div> <div id="p-help" class="vector-menu mw-portlet mw-portlet-help" > <div class="vector-menu-heading"> ヘルプ </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:%E7%9B%AE%E6%AC%A1" title="情報を得る場所"><span>ヘルプ</span></a></li><li id="n-villagepump" class="mw-list-item"><a href="/wiki/Wikipedia:%E4%BA%95%E6%88%B8%E7%AB%AF" title="プロジェクトについての意見交換"><span>井戸端</span></a></li><li id="n-notice" class="mw-list-item"><a href="/wiki/Wikipedia:%E3%81%8A%E7%9F%A5%E3%82%89%E3%81%9B" title="プロジェクトについてのお知らせ"><span>お知らせ</span></a></li><li id="n-bugreportspage" class="mw-list-item"><a href="/wiki/Wikipedia:%E3%83%90%E3%82%B0%E3%81%AE%E5%A0%B1%E5%91%8A" title="ウィキペディア・ソフトウェアのバグ報告"><span>バグの報告</span></a></li><li id="n-contact" class="mw-list-item"><a href="/wiki/Wikipedia:%E9%80%A3%E7%B5%A1%E5%85%88" title="ウィキペディアやウィキメディア財団に関する連絡先"><span>ウィキペディアに関するお問い合わせ</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/%E3%83%A1%E3%82%A4%E3%83%B3%E3%83%9A%E3%83%BC%E3%82%B8" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-ja.svg" style="width: 7.5em; height: 1.25em;"> <img class="mw-logo-tagline" alt="" src="/static/images/mobile/copyright/wikipedia-tagline-ja.svg" width="100" height="14" style="width: 6.25em; height: 0.875em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/%E7%89%B9%E5%88%A5:%E6%A4%9C%E7%B4%A2" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Wikipedia内を検索 [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>検索</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Wikipedia内を検索" aria-label="Wikipedia内を検索" autocapitalize="sentences" title="Wikipedia内を検索 [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="特別:検索"> </div> <button class="cdx-button cdx-search-input__end-button">検索</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="個人用ツール"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="表示"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="ページのフォントサイズ、幅、色の外観を変更する" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="表示" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">表示</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=ja.wikipedia.org&uselang=ja" class=""><span>寄付</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%82%A2%E3%82%AB%E3%82%A6%E3%83%B3%E3%83%88%E4%BD%9C%E6%88%90&returnto=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90+%28%E5%AE%87%E5%AE%99%E8%AB%96%29" title="アカウントを作成してログインすることをお勧めしますが、必須ではありません" class=""><span>アカウント作成</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%83%AD%E3%82%B0%E3%82%A4%E3%83%B3&returnto=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90+%28%E5%AE%87%E5%AE%99%E8%AB%96%29" title="ログインすることを推奨します。ただし、必須ではありません。 [o]" accesskey="o" class=""><span>ログイン</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="その他の操作" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="個人用ツール" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">個人用ツール</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="利用者メニュー" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=ja.wikipedia.org&uselang=ja"><span>寄付</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%82%A2%E3%82%AB%E3%82%A6%E3%83%B3%E3%83%88%E4%BD%9C%E6%88%90&returnto=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90+%28%E5%AE%87%E5%AE%99%E8%AB%96%29" title="アカウントを作成してログインすることをお勧めしますが、必須ではありません"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>アカウント作成</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%83%AD%E3%82%B0%E3%82%A4%E3%83%B3&returnto=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90+%28%E5%AE%87%E5%AE%99%E8%AB%96%29" title="ログインすることを推奨します。ただし、必須ではありません。 [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>ログイン</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> ログアウトした編集者のページ <a href="/wiki/Wikipedia:%E3%82%A6%E3%82%A3%E3%82%AD%E3%83%9A%E3%83%87%E3%82%A3%E3%82%A2%E3%81%B8%E3%82%88%E3%81%86%E3%81%93%E3%81%9D" aria-label="編集の詳細"><span>もっと詳しく</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E8%87%AA%E5%88%86%E3%81%AE%E6%8A%95%E7%A8%BF%E8%A8%98%E9%8C%B2" title="このIPアドレスからなされた編集の一覧 [y]" accesskey="y"><span>投稿記録</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E3%83%88%E3%83%BC%E3%82%AF%E3%83%9A%E3%83%BC%E3%82%B8" title="このIPアドレスからなされた編集についての議論 [n]" accesskey="n"><span>トーク</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="サイト"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目次" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目次</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">非表示</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">ページ先頭</div> </a> </li> <li id="toc-関連項目" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#関連項目"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>関連項目</span> </div> </a> <ul id="toc-関連項目-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-出典" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#出典"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>出典</span> </div> </a> <ul id="toc-出典-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参考文献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参考文献"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>参考文献</span> </div> </a> <ul id="toc-参考文献-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部リンク" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部リンク"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>外部リンク</span> </div> </a> <ul id="toc-外部リンク-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="目次" 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="目次の表示・非表示を切り替え" > <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">目次の表示・非表示を切り替え</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">スケール因子 (宇宙論)</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="特定の記事の別の言語版に移動します。利用可能な言語18件" > <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-18" 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">18の言語版</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%A7%D9%85%D9%84_%D8%AA%D8%AD%D8%AC%D9%8A%D9%85" title="アラビア語: عامل تحجيم" lang="ar" hreflang="ar" data-title="عامل تحجيم" data-language-autonym="العربية" data-language-local-name="アラビア語" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Factor_d%27escala" title="カタロニア語: Factor d'escala" lang="ca" hreflang="ca" data-title="Factor d'escala" data-language-autonym="Català" data-language-local-name="カタロニア語" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Skalenfaktor" title="ドイツ語: Skalenfaktor" lang="de" hreflang="de" data-title="Skalenfaktor" data-language-autonym="Deutsch" data-language-local-name="ドイツ語" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Scale_factor_(cosmology)" title="英語: Scale factor (cosmology)" lang="en" hreflang="en" data-title="Scale factor (cosmology)" data-language-autonym="English" data-language-local-name="英語" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Universa_skala_faktoro" title="エスペラント語: Universa skala faktoro" lang="eo" hreflang="eo" data-title="Universa skala faktoro" data-language-autonym="Esperanto" data-language-local-name="エスペラント語" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D8%A7%DA%A9%D8%AA%D9%88%D8%B1_%D9%85%D9%82%DB%8C%D8%A7%D8%B3" title="ペルシア語: فاکتور مقیاس" lang="fa" hreflang="fa" data-title="فاکتور مقیاس" data-language-autonym="فارسی" data-language-local-name="ペルシア語" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Skaalatekij%C3%A4" title="フィンランド語: Skaalatekijä" lang="fi" hreflang="fi" data-title="Skaalatekijä" data-language-autonym="Suomi" data-language-local-name="フィンランド語" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Facteur_d%27%C3%A9chelle" title="フランス語: Facteur d'échelle" lang="fr" hreflang="fr" data-title="Facteur d'échelle" data-language-autonym="Français" data-language-local-name="フランス語" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%A8%D7%9E%D7%98%D7%A8_%D7%94%D7%A1%D7%A7%D7%9C%D7%94_%D7%A9%D7%9C_%D7%94%D7%99%D7%A7%D7%95%D7%9D" title="ヘブライ語: פרמטר הסקלה של היקום" lang="he" hreflang="he" data-title="פרמטר הסקלה של היקום" data-language-autonym="עברית" data-language-local-name="ヘブライ語" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Fattore_di_scala" title="イタリア語: Fattore di scala" lang="it" hreflang="it" data-title="Fattore di scala" data-language-autonym="Italiano" data-language-local-name="イタリア語" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B2%99%EB%8F%84%EC%9D%B8%EC%9E%90" title="韓国語: 척도인자" lang="ko" hreflang="ko" data-title="척도인자" data-language-autonym="한국어" data-language-local-name="韓国語" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Czynnik_skali" title="ポーランド語: Czynnik skali" lang="pl" hreflang="pl" data-title="Czynnik skali" data-language-autonym="Polski" data-language-local-name="ポーランド語" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fator_de_escala_(cosmologia)" title="ポルトガル語: Fator de escala (cosmologia)" lang="pt" hreflang="pt" data-title="Fator de escala (cosmologia)" data-language-autonym="Português" data-language-local-name="ポルトガル語" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%81%D1%88%D1%82%D0%B0%D0%B1%D0%BD%D1%8B%D0%B9_%D0%BA%D0%BE%D1%8D%D1%84%D1%84%D0%B8%D1%86%D0%B8%D0%B5%D0%BD%D1%82_(%D0%BA%D0%BE%D1%81%D0%BC%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8%D1%8F)" title="ロシア語: Масштабный коэффициент (космология)" lang="ru" hreflang="ru" data-title="Масштабный коэффициент (космология)" data-language-autonym="Русский" data-language-local-name="ロシア語" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Skalirni_faktor_(kozmologija)" title="スロベニア語: Skalirni faktor (kozmologija)" lang="sl" hreflang="sl" data-title="Skalirni faktor (kozmologija)" data-language-autonym="Slovenščina" data-language-local-name="スロベニア語" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Skalfaktor" title="スウェーデン語: Skalfaktor" lang="sv" hreflang="sv" data-title="Skalfaktor" data-language-autonym="Svenska" data-language-local-name="スウェーデン語" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D1%81%D0%BC%D0%BE%D0%BB%D0%BE%D0%B3%D1%96%D1%87%D0%BD%D0%B8%D0%B9_%D0%BC%D0%B0%D1%81%D1%88%D1%82%D0%B0%D0%B1%D0%BD%D0%B8%D0%B9_%D1%84%D0%B0%D0%BA%D1%82%D0%BE%D1%80" title="ウクライナ語: Космологічний масштабний фактор" lang="uk" hreflang="uk" data-title="Космологічний масштабний фактор" data-language-autonym="Українська" data-language-local-name="ウクライナ語" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%AE%87%E5%AE%99%E6%A8%99%E5%BA%A6%E5%9B%A0%E5%AD%90" title="中国語: 宇宙標度因子" lang="zh" hreflang="zh" data-title="宇宙標度因子" data-language-autonym="中文" data-language-local-name="中国語" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1332997#sitelinks-wikipedia" title="言語間リンクを編集" class="wbc-editpage">リンクを編集</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="名前空間"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)" title="本文を閲覧 [c]" accesskey="c"><span>ページ</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%E3%83%8E%E3%83%BC%E3%83%88:%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)" rel="discussion" title="本文ページについての議論 [t]" accesskey="t"><span>ノート</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="別の言語に切り替える" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">日本語</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="表示"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)"><span>閲覧</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=edit" title="このページのソースコードを編集する [e]" accesskey="e"><span>編集</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=history" title="このページの過去の版 [h]" accesskey="h"><span>履歴表示</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="ページツール"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="ツール" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">ツール</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">ツール</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">非表示</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="その他の操作" > <div class="vector-menu-heading"> 操作 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)"><span>閲覧</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=edit" title="このページのソースコードを編集する [e]" accesskey="e"><span>編集</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=history"><span>履歴表示</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 全般 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E3%83%AA%E3%83%B3%E3%82%AF%E5%85%83/%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)" title="ここにリンクしている全ウィキページの一覧 [j]" accesskey="j"><span>リンク元</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E9%96%A2%E9%80%A3%E3%83%9A%E3%83%BC%E3%82%B8%E3%81%AE%E6%9B%B4%E6%96%B0%E7%8A%B6%E6%B3%81/%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)" rel="nofollow" title="このページからリンクしているページの最近の更新 [k]" accesskey="k"><span>関連ページの更新状況</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB%E3%81%AE%E3%82%A2%E3%83%83%E3%83%97%E3%83%AD%E3%83%BC%E3%83%89" title="ファイルをアップロードする [u]" accesskey="u"><span>ファイルをアップロード</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E7%89%B9%E5%88%A5%E3%83%9A%E3%83%BC%E3%82%B8%E4%B8%80%E8%A6%A7" title="特別ページの一覧 [q]" accesskey="q"><span>特別ページ</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&oldid=101661688" title="このページのこの版への固定リンク"><span>この版への固定リンク</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=info" title="このページについての詳細情報"><span>ページ情報</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%81%93%E3%81%AE%E3%83%9A%E3%83%BC%E3%82%B8%E3%82%92%E5%BC%95%E7%94%A8&page=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_%28%E5%AE%87%E5%AE%99%E8%AB%96%29&id=101661688&wpFormIdentifier=titleform" title="このページの引用方法"><span>このページを引用</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:UrlQ%C4%B1sald%C4%B1c%C4%B1s%C4%B1&url=https%3A%2F%2Fja.wikipedia.org%2Fwiki%2F%25E3%2582%25B9%25E3%2582%25B1%25E3%2583%25BC%25E3%2583%25AB%25E5%259B%25A0%25E5%25AD%2590_%28%25E5%25AE%2587%25E5%25AE%2599%25E8%25AB%2596%29"><span>短縮URLを取得する</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:QrKodu&url=https%3A%2F%2Fja.wikipedia.org%2Fwiki%2F%25E3%2582%25B9%25E3%2582%25B1%25E3%2583%25BC%25E3%2583%25AB%25E5%259B%25A0%25E5%25AD%2590_%28%25E5%25AE%2587%25E5%25AE%2599%25E8%25AB%2596%29"><span>QRコードをダウンロード</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> 印刷/書き出し </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%83%96%E3%83%83%E3%82%AF&bookcmd=book_creator&referer=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90+%28%E5%AE%87%E5%AE%99%E8%AB%96%29"><span>ブックの新規作成</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:DownloadAsPdf&page=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_%28%E5%AE%87%E5%AE%99%E8%AB%96%29&action=show-download-screen"><span>PDF 形式でダウンロード</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&printable=yes" title="このページの印刷用ページ [p]" accesskey="p"><span>印刷用バージョン</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 他のプロジェクト </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1332997" title="関連付けられたデータリポジトリ項目へのリンク [g]" accesskey="g"><span>ウィキデータ項目</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="ページツール"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="表示"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">表示</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">非表示</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">出典: フリー百科事典『ウィキペディア（Wikipedia）』</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ja" dir="ltr"><p><a href="/wiki/%E5%AE%87%E5%AE%99%E8%AB%96" title="宇宙論">宇宙論</a>における<b>スケール因子</b>（スケールいんし、<a href="/wiki/%E8%8B%B1%E8%AA%9E" title="英語">英</a>: <span lang="en">scale factor</span>）は、しばしば<b>宇宙膨張因子</b>、あるいは単に<b>膨張因子</b>、さらには<a href="/wiki/%E3%83%95%E3%83%AA%E3%83%BC%E3%83%89%E3%83%9E%E3%83%B3%E6%96%B9%E7%A8%8B%E5%BC%8F" title="フリードマン方程式">フリードマン方程式</a>における<a href="/wiki/%E3%83%95%E3%83%AA%E3%83%BC%E3%83%89%E3%83%9E%E3%83%B3%E3%83%BB%E3%83%AB%E3%83%A1%E3%83%BC%E3%83%88%E3%83%AB%E3%83%BB%E3%83%AD%E3%83%90%E3%83%BC%E3%83%88%E3%82%BD%E3%83%B3%E3%83%BB%E3%82%A6%E3%82%A9%E3%83%BC%E3%82%AB%E3%83%BC%E8%A8%88%E9%87%8F" title="フリードマン・ルメートル・ロバートソン・ウォーカー計量">フリードマン・ルメートル・ロバートソン・ウォーカー計量</a>（FLRW 計量）パラメータ<sup id="cite_ref-FOOTNOTEWeinberg20083_1-0" class="reference"><a href="#cite_note-FOOTNOTEWeinberg20083-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>とも呼ばれ、<a href="/wiki/%E3%83%93%E3%83%83%E3%82%B0%E3%83%90%E3%83%B3" title="ビッグバン">膨張する宇宙の計量</a>における<a href="/wiki/%E6%99%82%E9%96%93" title="時間">時間</a>の<a href="/wiki/%E9%96%A2%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="関数 (数学)">関数</a>である。これは 2 つの<a href="/wiki/%E7%89%A9%E4%BD%93" title="物体">物体</a>間、例えば<a href="/wiki/%E3%83%8F%E3%83%83%E3%83%96%E3%83%AB%E3%81%AE%E6%B3%95%E5%89%87" class="mw-redirect" title="ハッブルの法則">ハッブルの法則</a>に従って離れていく 2 つの<a href="/wiki/%E9%8A%80%E6%B2%B3%E5%9B%A3" title="銀河団">銀河団</a>間などの固有の<a href="/wiki/%E8%B7%9D%E9%9B%A2" title="距離">距離</a>（時間とともに変化できるが、一定となる<a href="/wiki/%E5%85%B1%E5%8B%95%E8%B7%9D%E9%9B%A2" class="mw-redirect" title="共動距離">共動距離</a>とは異なる）と関係する。ある基準となる時刻 <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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02d3006c4190b1939b04d9b9bb21006fb4e6fa4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{0}}"></span> での距離に対して任意の時刻 <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> での FLRW 計量の宇宙膨張をいう。これは次式で与えられる。 </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 d(t)=a(t)d_{0}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d(t)=a(t)d_{0}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f12810f6ea46724bab86d2c08171756371f3be88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.139ex; height:2.843ex;" alt="{\displaystyle d(t)=a(t)d_{0}.\,}"></span></dd></dl> <p>ここで、<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 d(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e115e742b9743138b3f4c1fd7cf9c7263dcdbe43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.865ex; height:2.843ex;" alt="{\displaystyle d(t)}"></span> はある時刻 <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> での固有距離、<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 d_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4740381c16ea98c4132510daa642e93c1e42c049" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.263ex; height:2.509ex;" alt="{\displaystyle d_{0}}"></span> は基準とする時刻 <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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02d3006c4190b1939b04d9b9bb21006fb4e6fa4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{0}}"></span> での距離で、<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(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb7931a26b0d360eaf90aa45247d2de5c984d5d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.879ex; height:2.843ex;" alt="{\displaystyle a(t)}"></span> がスケール因子である<sup id="cite_ref-FOOTNOTESchutz2003363_2-0" class="reference"><a href="#cite_note-FOOTNOTESchutz2003363-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>。この定義により、<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(t_{0})=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo stretchy="false">(</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a(t_{0})=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b58ed1994b4bea79c6d38529fc4018f12f8f21ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.194ex; height:2.843ex;" alt="{\displaystyle a(t_{0})=1}"></span> となる。 </p><p>スケール因子は<a href="/wiki/%E7%84%A1%E6%AC%A1%E5%85%83%E9%87%8F" title="無次元量">無次元量</a>であり、宇宙誕生からの時刻 <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> 、宇宙の年齢を表す <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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02d3006c4190b1939b04d9b9bb21006fb4e6fa4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{0}}"></span> = 137.98±0.37 億年（2013年現在）<sup id="cite_ref-FOOTNOTEPlanck_collaboration2013_3-0" class="reference"><a href="#cite_note-FOOTNOTEPlanck_collaboration2013-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>を用いて、現在の <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> の値は <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(t_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo stretchy="false">(</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a(t_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6274bf1d32a349c6f27aeb758f3042bcd3c74049" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.933ex; height:2.843ex;" alt="{\displaystyle a(t_{0})}"></span> または <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 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span> と与えられている。 </p><p>ダイナミックな問いであるスケール因子の進化は<a href="/wiki/%E4%B8%80%E8%88%AC%E7%9B%B8%E5%AF%BE%E6%80%A7%E7%90%86%E8%AB%96" title="一般相対性理論">一般相対性理論</a>の方程式で決定され、これは宇宙が局所的に等方的で均質な場合の<a href="/wiki/%E3%83%95%E3%83%AA%E3%83%BC%E3%83%89%E3%83%9E%E3%83%B3%E6%96%B9%E7%A8%8B%E5%BC%8F" title="フリードマン方程式">フリードマン方程式</a>により表される。 </p><p><a href="/wiki/%E3%83%8F%E3%83%83%E3%83%96%E3%83%AB%E5%AE%9A%E6%95%B0" class="mw-redirect" title="ハッブル定数">ハッブル定数</a>は以下のように定義される。： </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 H\equiv {{\dot {a}}(t) \over a(t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>≡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>a</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H\equiv {{\dot {a}}(t) \over a(t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/886e67558bc0ee40caf49ce2adec5f5df67089b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:9.877ex; height:6.509ex;" alt="{\displaystyle H\equiv {{\dot {a}}(t) \over a(t)}}"></span></dd></dl> <p>ここで、<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> の<a href="/wiki/%E3%83%8B%E3%83%A5%E3%83%BC%E3%83%88%E3%83%B3%E3%81%AE%E8%A8%98%E6%B3%95" title="ニュートンの記法">上付きの点</a>は <a href="/wiki/%E6%99%82%E9%96%93%E5%BE%AE%E5%88%86" title="時間微分">時間微分</a>である。 </p><p>前述の式 <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 d(t)=d_{0}a(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>a</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d(t)=d_{0}a(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d16152f881a86d0da4aebc5079dabefe2167b24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.105ex; height:2.843ex;" alt="{\displaystyle d(t)=d_{0}a(t)}"></span> から、<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 {\dot {d}}(t)=d_{0}{\dot {a}}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>d</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {d}}(t)=d_{0}{\dot {a}}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a59458ae506a5b1fe2c671011e0a10931058d7b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.471ex; height:3.176ex;" alt="{\displaystyle {\dot {d}}(t)=d_{0}{\dot {a}}(t)}"></span> とみなすことができ、また <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 d_{0}={\frac {d(t)}{a(t)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>a</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{0}={\frac {d(t)}{a(t)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83133a53e62569f6e87e5c999ac0755fb6c381c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:10.076ex; height:6.509ex;" alt="{\displaystyle d_{0}={\frac {d(t)}{a(t)}}}"></span> でもあることから、これらを組み合わせて <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 {\dot {d}}(t)={\frac {d(t){\dot {a}}(t)}{a(t)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>d</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>a</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {d}}(t)={\frac {d(t){\dot {a}}(t)}{a(t)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7018fc58f4bc6d227ca1450b59315dcd1fdd323" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:15.909ex; height:6.509ex;" alt="{\displaystyle {\dot {d}}(t)={\frac {d(t){\dot {a}}(t)}{a(t)}}}"></span> が与えられ、上記のハッブルパラメータの定義に代入すれば、 <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 {\dot {d}}(t)=Hd(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>d</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>H</mi> <mi>d</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {d}}(t)=Hd(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8d9bb51755ca8313e4298efbaafd7533552a7ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.257ex; height:3.176ex;" alt="{\displaystyle {\dot {d}}(t)=Hd(t)}"></span> となり、これはハッブル則である。 </p><p>現在の観測結果による証拠は、<a href="/wiki/%E5%AE%87%E5%AE%99%E3%81%AE%E5%8A%A0%E9%80%9F" class="mw-redirect" title="宇宙の加速">宇宙の膨張率が加速している</a>ことを示唆している。このことはスケール因子の2階微分 <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}}(t)}"> <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 stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ddot {a}}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d2c78880b23f3563c08d7f59eed8ff2bb5092b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.879ex; height:2.843ex;" alt="{\displaystyle {\ddot {a}}(t)}"></span> が正であることを意味する。または、1階微分 <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 {\dot {a}}(t)}"> <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 stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {a}}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b535a576516092ae1bad491d6586fedb359ff47b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.879ex; height:2.843ex;" alt="{\displaystyle {\dot {a}}(t)}"></span> が時間を追って増大していることと等価であることを示す<sup id="cite_ref-FOOTNOTEJonesLambourne2004244_4-0" class="reference"><a href="#cite_note-FOOTNOTEJonesLambourne2004244-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>。あるいは、任意の銀河が時間を追って速さを増し我々から遠ざかっていること、すなわち銀河の <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 {\dot {d}}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>d</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {d}}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90ad1660abae0ee20472aa01fe49bd57b4f73773" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.231ex; height:3.176ex;" alt="{\displaystyle {\dot {d}}(t)}"></span> が時間を掛けて増大していることを意味している。対照的に、ハッブル定数は時間とともに“減少”しているようにみえる。これは我々が“固定された”距離 <span lang="en" class="texhtml mvar" style="font-style:italic;">d</span> から別々の銀河の列がこの距離を通過するのを眺めた場合、先に進んでいた銀河よりも小さい速度で後からの銀河が進んでいくように見えることになる<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>。 </p><p>膨張宇宙モデルとして使われる<a href="/wiki/%E3%83%95%E3%83%AA%E3%83%BC%E3%83%89%E3%83%9E%E3%83%B3%E3%83%BB%E3%83%AB%E3%83%A1%E3%83%BC%E3%83%88%E3%83%AB%E3%83%BB%E3%83%AD%E3%83%90%E3%83%BC%E3%83%88%E3%82%BD%E3%83%B3%E3%83%BB%E3%82%A6%E3%82%A9%E3%83%BC%E3%82%AB%E3%83%BC%E8%A8%88%E9%87%8F" title="フリードマン・ルメートル・ロバートソン・ウォーカー計量">フリードマン・ルメートル・ロバートソン・ウォーカー計量</a>によれば、現在の時刻に赤方偏移 z を示す遠く離れた物体からの光が届くと、もともとの光を放射している物体のその時刻でのスケールファクタは <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(t)={\frac {1}{1+z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <mi>z</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a(t)={\frac {1}{1+z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fc50f64b94c0a8d7356a0726ca0a303db1c8b95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.904ex; height:5.343ex;" alt="{\displaystyle a(t)={\frac {1}{1+z}}}"></span> となる<sup id="cite_ref-FOOTNOTEDavies1992187_6-0" class="reference"><a href="#cite_note-FOOTNOTEDavies1992187-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEMukhanov200558_7-0" class="reference"><a href="#cite_note-FOOTNOTEMukhanov200558-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="関連項目"><span id=".E9.96.A2.E9.80.A3.E9.A0.85.E7.9B.AE"></span>関連項目</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=edit&section=1" title="節を編集: 関連項目"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E3%83%95%E3%83%AA%E3%83%BC%E3%83%89%E3%83%9E%E3%83%B3%E6%96%B9%E7%A8%8B%E5%BC%8F" title="フリードマン方程式">フリードマン方程式</a></li> <li><a href="/wiki/%E3%83%95%E3%83%AA%E3%83%BC%E3%83%89%E3%83%9E%E3%83%B3%E3%83%BB%E3%83%AB%E3%83%A1%E3%83%BC%E3%83%88%E3%83%AB%E3%83%BB%E3%83%AD%E3%83%90%E3%83%BC%E3%83%88%E3%82%BD%E3%83%B3%E3%83%BB%E3%82%A6%E3%82%A9%E3%83%BC%E3%82%AB%E3%83%BC%E8%A8%88%E9%87%8F" title="フリードマン・ルメートル・ロバートソン・ウォーカー計量">フリードマン・ルメートル・ロバートソン・ウォーカー計量</a></li> <li><a href="/wiki/%E8%B5%A4%E6%96%B9%E5%81%8F%E7%A7%BB" title="赤方偏移">赤方偏移</a></li> <li><a href="/wiki/%E5%AE%87%E5%AE%99%E5%8E%9F%E7%90%86" title="宇宙原理">宇宙原理</a></li> <li><a href="/wiki/%CE%9B-CDM%E3%83%A2%E3%83%87%E3%83%AB" title="Λ-CDMモデル">Λ-CDMモデル</a></li> <li><a href="/wiki/%E3%83%8F%E3%83%83%E3%83%96%E3%83%AB%E3%81%AE%E6%B3%95%E5%89%87" class="mw-redirect" title="ハッブルの法則">ハッブルの法則</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="出典"><span id=".E5.87.BA.E5.85.B8"></span>出典</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=edit&section=2" title="節を編集: 出典"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-FOOTNOTEWeinberg20083-1"><b><a href="#cite_ref-FOOTNOTEWeinberg20083_1-0">^</a></b> <span class="reference-text"><a href="#CITEREFWeinberg2008">Weinberg 2008</a>, p. 3.</span> </li> <li id="cite_note-FOOTNOTESchutz2003363-2"><b><a href="#cite_ref-FOOTNOTESchutz2003363_2-0">^</a></b> <span class="reference-text"><a href="#CITEREFSchutz2003">Schutz 2003</a>, p. 363.</span> </li> <li id="cite_note-FOOTNOTEPlanck_collaboration2013-3"><b><a href="#cite_ref-FOOTNOTEPlanck_collaboration2013_3-0">^</a></b> <span class="reference-text"><a href="#CITEREFPlanck_collaboration2013">Planck collaboration 2013</a>.</span> </li> <li id="cite_note-FOOTNOTEJonesLambourne2004244-4"><b><a href="#cite_ref-FOOTNOTEJonesLambourne2004244_4-0">^</a></b> <span class="reference-text"><a href="#CITEREFJonesLambourne2004">Jones & Lambourne 2004</a>, p. 244.</span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text"><a rel="nofollow" class="external text" href="http://curious.astro.cornell.edu/question.php?number=575">Is the universe expanding faster than the speed of light?</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20031123150109/http://curious.astro.cornell.edu/question.php?number=575">Archived</a> 2003年11月23日, at the <a href="/wiki/%E3%82%A6%E3%82%A7%E3%82%A4%E3%83%90%E3%83%83%E3%82%AF%E3%83%9E%E3%82%B7%E3%83%B3" title="ウェイバックマシン">Wayback Machine</a>. (最終節を参照)</span> </li> <li id="cite_note-FOOTNOTEDavies1992187-6"><b><a href="#cite_ref-FOOTNOTEDavies1992187_6-0">^</a></b> <span class="reference-text"><a href="#CITEREFDavies1992">Davies 1992</a>, p. 187.</span> </li> <li id="cite_note-FOOTNOTEMukhanov200558-7"><b><a href="#cite_ref-FOOTNOTEMukhanov200558_7-0">^</a></b> <span class="reference-text"><a href="#CITEREFMukhanov2005">Mukhanov 2005</a>, p. 58.</span> </li> </ol> <div class="mw-heading mw-heading2"><h2 id="参考文献"><span id=".E5.8F.82.E8.80.83.E6.96.87.E7.8C.AE"></span>参考文献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=edit&section=3" title="節を編集: 参考文献"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite style="font-style:normal" class="citation book" id="CITEREFWeinberg2008">Weinberg, Steven (2008). <a rel="nofollow" class="external text" href="https://books.google.co.jp/books?id=48C-ym2EmZkC&pg=PA3&redir_esc=y&hl=ja"><i>Cosmology</i></a>. Oxford University Press. p. 3. <style data-mw-deduplicate="TemplateStyles:r101121245">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation.cs-ja1 q,.mw-parser-output .citation.cs-ja2 q{quotes:"「""」""『""』"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-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 a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-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 a,.mw-parser-output .citation .cs1-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}.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:var(--color-success,#3a3);margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.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}</style><a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%E7%89%B9%E5%88%A5:%E6%96%87%E7%8C%AE%E8%B3%87%E6%96%99/978-0-19-852682-7" title="特別:文献資料/978-0-19-852682-7">978-0-19-852682-7</a><span style="display:none;">. <a rel="nofollow" class="external free" href="https://books.google.co.jp/books?id=48C-ym2EmZkC&pg=PA3&redir_esc=y&hl=ja">https://books.google.co.jp/books?id=48C-ym2EmZkC&pg=PA3&redir_esc=y&hl=ja</a></span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cosmology&rft.aulast=Weinberg&rft.aufirst=Steven&rft.au=Weinberg%2C%26%2332%3BSteven&rft.date=2008&rft.pages=p.%26nbsp%3B3&rft.pub=Oxford+University+Press&rft.isbn=978-0-19-852682-7&rft_id=https%3A%2F%2Fbooks.google.co.jp%2Fbooks%3Fid%3D48C-ym2EmZkC%26pg%3DPA3%26redir_esc%3Dy%26hl%3Dja&rfr_id=info:sid/ja.wikipedia.org:%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)"><span style="display: none;"> </span></span></li> <li><cite style="font-style:normal" class="citation book" id="CITEREFSchutz2003">Schutz, Bernard (2003). <a rel="nofollow" class="external text" href="https://books.google.co.jp/books?id=iEZNXvYwyNwC&lpg=PP1&pg=PA363&redir_esc=y&hl=ja#v=onepage&q&f=false"><i>Gravity from the Ground Up: An Introductory Guide to Gravity and General Relativity</i></a>. Cambridge University Press. p. 363. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101121245"><a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%E7%89%B9%E5%88%A5:%E6%96%87%E7%8C%AE%E8%B3%87%E6%96%99/978-0-521-45506-0" title="特別:文献資料/978-0-521-45506-0">978-0-521-45506-0</a><span style="display:none;">. <a rel="nofollow" class="external free" href="https://books.google.co.jp/books?id=iEZNXvYwyNwC&lpg=PP1&pg=PA363&redir_esc=y&hl=ja#v=onepage&q&f=false">https://books.google.co.jp/books?id=iEZNXvYwyNwC&lpg=PP1&pg=PA363&redir_esc=y&hl=ja#v=onepage&q&f=false</a></span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gravity+from+the+Ground+Up%3A+An+Introductory+Guide+to+Gravity+and+General+Relativity&rft.aulast=Schutz&rft.aufirst=Bernard&rft.au=Schutz%2C%26%2332%3BBernard&rft.date=2003&rft.pages=p.%26nbsp%3B363&rft.pub=Cambridge+University+Press&rft.isbn=978-0-521-45506-0&rft_id=https%3A%2F%2Fbooks.google.co.jp%2Fbooks%3Fid%3DiEZNXvYwyNwC%26lpg%3DPP1%26pg%3DPA363%26redir_esc%3Dy%26hl%3Dja%23v%3Donepage%26q%26f%3Dfalse&rfr_id=info:sid/ja.wikipedia.org:%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)"><span style="display: none;"> </span></span></li> <li><cite style="font-style:normal" class="citation journal" id="CITEREFPlanck_collaboration2013">Planck collaboration (2013). “Planck 2013 results. I. Overview of products and scientific results”. <i>Submitted to Astronomy & Astrophysics</i>. <a href="/wiki/ArXiv_(%E8%AD%98%E5%88%A5%E5%AD%90)" class="mw-redirect" title="ArXiv (識別子)">arXiv</a>:<a href="https://arxiv.org/abs/1303.5062" class="extiw" title="arxiv:1303.5062">1303.5062</a>. <a href="/wiki/Bibcode_(%E8%AD%98%E5%88%A5%E5%AD%90)" class="mw-redirect" title="Bibcode (識別子)">Bibcode</a>: <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013arXiv1303.5062P/abstract">2013arXiv1303.5062P</a>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Planck+2013+results.+I.+Overview+of+products+and+scientific+results&rft.jtitle=Submitted+to+Astronomy+%26+Astrophysics&rft.aulast=Planck+collaboration&rft.au=Planck+collaboration&rft.date=2013&rft_id=info:arxiv/1303.5062&rft_id=info:bibcode/2013arXiv1303.5062P&rfr_id=info:sid/ja.wikipedia.org:%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)"><span style="display: none;"> </span></span></li> <li><cite style="font-style:normal" class="citation book" id="CITEREFJonesLambourne2004">Jones, Mark H.; Lambourne, Robert J. (2004). <a rel="nofollow" class="external text" href="https://books.google.co.jp/books?id=36K1PfetZegC&lpg=PP1&pg=PA244&redir_esc=y&hl=ja#v=onepage&q&f=false"><i>An Introduction to Galaxies and Cosmology</i></a>. Cambridge University Press. p. 244. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101121245"><a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%E7%89%B9%E5%88%A5:%E6%96%87%E7%8C%AE%E8%B3%87%E6%96%99/978-0-521-83738-5" title="特別:文献資料/978-0-521-83738-5">978-0-521-83738-5</a><span style="display:none;">. <a rel="nofollow" class="external free" href="https://books.google.co.jp/books?id=36K1PfetZegC&lpg=PP1&pg=PA244&redir_esc=y&hl=ja#v=onepage&q&f=false">https://books.google.co.jp/books?id=36K1PfetZegC&lpg=PP1&pg=PA244&redir_esc=y&hl=ja#v=onepage&q&f=false</a></span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Galaxies+and+Cosmology&rft.aulast=Jones&rft.aufirst=Mark+H.&rft.au=Jones%2C%26%2332%3BMark+H.&rft.au=Lambourne%2C%26%2332%3BRobert+J.&rft.date=2004&rft.pages=p.%26nbsp%3B244&rft.pub=Cambridge+University+Press&rft.isbn=978-0-521-83738-5&rft_id=https%3A%2F%2Fbooks.google.co.jp%2Fbooks%3Fid%3D36K1PfetZegC%26lpg%3DPP1%26pg%3DPA244%26redir_esc%3Dy%26hl%3Dja%23v%3Donepage%26q%26f%3Dfalse&rfr_id=info:sid/ja.wikipedia.org:%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)"><span style="display: none;"> </span></span></li> <li><cite style="font-style:normal" class="citation book" id="CITEREFDavies1992">Davies, Paul (1992). <a rel="nofollow" class="external text" href="https://books.google.co.jp/books?id=akb2FpZSGnMC&lpg=PP1&pg=PA187&redir_esc=y&hl=ja#v=onepage&q&f=false"><i>The New Physics</i></a>. p. 187<span style="display:none;">. <a rel="nofollow" class="external free" href="https://books.google.co.jp/books?id=akb2FpZSGnMC&lpg=PP1&pg=PA187&redir_esc=y&hl=ja#v=onepage&q&f=false">https://books.google.co.jp/books?id=akb2FpZSGnMC&lpg=PP1&pg=PA187&redir_esc=y&hl=ja#v=onepage&q&f=false</a></span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+New+Physics&rft.aulast=Davies&rft.aufirst=Paul&rft.au=Davies%2C%26%2332%3BPaul&rft.date=1992&rft.pages=p.%26nbsp%3B187&rft_id=https%3A%2F%2Fbooks.google.co.jp%2Fbooks%3Fid%3Dakb2FpZSGnMC%26lpg%3DPP1%26pg%3DPA187%26redir_esc%3Dy%26hl%3Dja%23v%3Donepage%26q%26f%3Dfalse&rfr_id=info:sid/ja.wikipedia.org:%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)"><span style="display: none;"> </span></span></li> <li><cite style="font-style:normal" class="citation book" id="CITEREFMukhanov2005">Mukhanov, V. F. (2005). <a rel="nofollow" class="external text" href="https://books.google.co.jp/books?id=1TXO7GmwZFgC&lpg=PP1&pg=PA58&redir_esc=y&hl=ja#v=onepage&q&f=false"><i>Physical Foundations of Cosmology</i></a>. p. 58<span style="display:none;">. <a rel="nofollow" class="external free" href="https://books.google.co.jp/books?id=1TXO7GmwZFgC&lpg=PP1&pg=PA58&redir_esc=y&hl=ja#v=onepage&q&f=false">https://books.google.co.jp/books?id=1TXO7GmwZFgC&lpg=PP1&pg=PA58&redir_esc=y&hl=ja#v=onepage&q&f=false</a></span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physical+Foundations+of+Cosmology&rft.aulast=Mukhanov&rft.aufirst=V.+F.&rft.au=Mukhanov%2C%26%2332%3BV.+F.&rft.date=2005&rft.pages=p.%26nbsp%3B58&rft_id=https%3A%2F%2Fbooks.google.co.jp%2Fbooks%3Fid%3D1TXO7GmwZFgC%26lpg%3DPP1%26pg%3DPA58%26redir_esc%3Dy%26hl%3Dja%23v%3Donepage%26q%26f%3Dfalse&rfr_id=info:sid/ja.wikipedia.org:%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)"><span style="display: none;"> </span></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="外部リンク"><span id=".E5.A4.96.E9.83.A8.E3.83.AA.E3.83.B3.E3.82.AF"></span>外部リンク</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=edit&section=4" title="節を編集: 外部リンク"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.astro.ucla.edu/~wright/cosmo_03.htm">Relation of the scale factor with the cosmological constant and the Hubble constant</a></li></ul> <style data-mw-deduplicate="TemplateStyles:r96783592">.mw-parser-output .asbox{position:relative;overflow:hidden}.mw-parser-output .asbox table{background:transparent}.mw-parser-output .asbox p{margin:0}.mw-parser-output .asbox p+p{margin-top:0.25em}.mw-parser-output .asbox{font-size:90%}.mw-parser-output .asbox-note{font-size:90%}.mw-parser-output .asbox .navbar{position:absolute;top:-0.90em;right:1em;display:none}</style><div role="note" class="metadata plainlinks asbox stub"><table role="presentation"><tbody><tr class="noresize"><td><span typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Nuvola_apps_kalzium.png" class="mw-file-description"><img alt="スタブアイコン" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Nuvola_apps_kalzium.png/30px-Nuvola_apps_kalzium.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Nuvola_apps_kalzium.png/45px-Nuvola_apps_kalzium.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Nuvola_apps_kalzium.png/60px-Nuvola_apps_kalzium.png 2x" data-file-width="128" data-file-height="128" /></a></span></td><td><p class="asbox-body">この項目は、<a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%A6" title="物理学">物理学</a>に関連した<b><a href="/wiki/Wikipedia:%E3%82%B9%E3%82%BF%E3%83%96" title="Wikipedia:スタブ">書きかけの項目</a></b>です。<a class="external text" href="https://ja.wikipedia.org/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=edit">この項目を加筆・訂正</a>などしてくださる<a href="/wiki/Category:%E7%89%A9%E7%90%86%E5%AD%A6%E9%96%A2%E9%80%A3%E3%81%AE%E3%82%B9%E3%82%BF%E3%83%96%E9%A0%85%E7%9B%AE" title="Category:物理学関連のスタブ項目">協力者を求めています</a>（<a href="/wiki/%E3%83%97%E3%83%AD%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88:%E7%89%A9%E7%90%86%E5%AD%A6" title="プロジェクト:物理学">プロジェクト:物理学</a>／<a href="/wiki/Portal:%E7%89%A9%E7%90%86%E5%AD%A6" title="Portal:物理学">Portal:物理学</a>）。</p></td></tr></tbody></table><style data-mw-deduplicate="TemplateStyles:r99966302">.mw-parser-output .hlist ul,.mw-parser-output .hlist ol{padding-left:0}.mw-parser-output .hlist li,.mw-parser-output .hlist dd,.mw-parser-output .hlist dt{margin-right:0;display:inline-block;white-space:nowrap}.mw-parser-output .hlist dt:after,.mw-parser-output .hlist dd:after,.mw-parser-output .hlist li:after{white-space:normal}.mw-parser-output .hlist li:after,.mw-parser-output .hlist dd:after{content:" ·\a0 ";font-weight:bold}.mw-parser-output .hlist dt:after{content:": "}.mw-parser-output .hlist-pipe dd:after,.mw-parser-output .hlist-pipe li:after{content:" |\a0 ";font-weight:normal}.mw-parser-output .hlist-hyphen dd:after,.mw-parser-output .hlist-hyphen li:after{content:" -\a0 ";font-weight:normal}.mw-parser-output .hlist-comma dd:after,.mw-parser-output .hlist-comma li:after{content:"、";font-weight:normal}.mw-parser-output .hlist-slash dd:after,.mw-parser-output .hlist-slash li:after{content:" /\a0 ";font-weight:normal}.mw-parser-output .hlist dd:last-child:after,.mw-parser-output .hlist dt:last-child:after,.mw-parser-output .hlist li:last-child:after{content:none}.mw-parser-output .hlist dd dd:first-child:before,.mw-parser-output .hlist dd dt:first-child:before,.mw-parser-output .hlist dd li:first-child:before,.mw-parser-output .hlist dt dd:first-child:before,.mw-parser-output .hlist dt dt:first-child:before,.mw-parser-output .hlist dt li:first-child:before,.mw-parser-output .hlist li dd:first-child:before,.mw-parser-output .hlist li dt:first-child:before,.mw-parser-output .hlist li li:first-child:before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child:after,.mw-parser-output .hlist dd dt:last-child:after,.mw-parser-output .hlist dd li:last-child:after,.mw-parser-output .hlist dt dd:last-child:after,.mw-parser-output .hlist dt dt:last-child:after,.mw-parser-output .hlist dt li:last-child:after,.mw-parser-output .hlist li dd:last-child:after,.mw-parser-output .hlist li dt:last-child:after,.mw-parser-output .hlist li li:last-child:after{content:")\a0 ";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li:before{content:" "counter(listitem)" ";white-space:nowrap}.mw-parser-output .hlist dd ol>li:first-child:before,.mw-parser-output .hlist dt ol>li:first-child:before,.mw-parser-output .hlist li ol>li:first-child:before{content:" ("counter(listitem)" "}</style><style data-mw-deduplicate="TemplateStyles:r96787822">.mw-parser-output .navbar{display:inline;font-size:75%;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-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}.mw-parser-output .infobox .navbar{font-size:88%}.mw-parser-output .navbox .navbar{display:block;font-size:88%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style><div class="navbar plainlinks hlist"><ul><li class="nv-view"><a href="/wiki/Template:Physics-stub" title="Template:Physics-stub"><span title="参照先のページを表示します。">表示</span></a></li><li class="nv-edit"><a class="external text" href="https://ja.wikipedia.org/w/index.php?title=Template:Physics-stub&action=edit"><span title="参照先のページを編集します。">編集</span></a></li></ul></div></div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r96783592"><div role="note" class="metadata plainlinks asbox stub"><table role="presentation"><tbody><tr class="noresize"><td><span typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:E-to-the-i-pi.svg" class="mw-file-description"><img alt="スタブアイコン" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/34px-E-to-the-i-pi.svg.png" decoding="async" width="34" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/51px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/68px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span></td><td><p class="asbox-body">この項目は、<a href="/wiki/%E6%95%B0%E5%AD%A6" title="数学">数学</a>に関連した<b><a href="/wiki/Wikipedia:%E3%82%B9%E3%82%BF%E3%83%96" title="Wikipedia:スタブ">書きかけの項目</a></b>です。<a class="external text" href="https://ja.wikipedia.org/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&action=edit">この項目を加筆・訂正</a>などしてくださる<a href="/wiki/Category:%E6%95%B0%E5%AD%A6%E9%96%A2%E9%80%A3%E3%81%AE%E3%82%B9%E3%82%BF%E3%83%96%E9%A0%85%E7%9B%AE" title="Category:数学関連のスタブ項目">協力者を求めています</a>（<a href="/wiki/%E3%83%97%E3%83%AD%E3%82%B8%E3%82%A7%E3%82%AF%E3%83%88:%E6%95%B0%E5%AD%A6" title="プロジェクト:数学">プロジェクト:数学</a>／<a href="/wiki/Portal:%E6%95%B0%E5%AD%A6" title="Portal:数学">Portal:数学</a>）。</p></td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r99966302"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r96787822"><div class="navbar plainlinks hlist"><ul><li class="nv-view"><a href="/wiki/Template:Math-stub" title="Template:Math-stub"><span title="参照先のページを表示します。">表示</span></a></li><li class="nv-edit"><a class="external text" href="https://ja.wikipedia.org/w/index.php?title=Template:Math-stub&action=edit"><span title="参照先のページを編集します。">編集</span></a></li></ul></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">「<a dir="ltr" href="https://ja.wikipedia.org/w/index.php?title=スケール因子_(宇宙論)&oldid=101661688">https://ja.wikipedia.org/w/index.php?title=スケール因子_(宇宙論)&oldid=101661688</a>」から取得</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%E7%89%B9%E5%88%A5:%E3%82%AB%E3%83%86%E3%82%B4%E3%83%AA" title="特別:カテゴリ">カテゴリ</a>: <ul><li><a href="/wiki/Category:%E5%AE%87%E5%AE%99%E8%AB%96" title="Category:宇宙論">宇宙論</a></li><li><a href="/wiki/Category:%E6%95%B0%E5%AD%A6%E3%81%AB%E9%96%A2%E3%81%99%E3%82%8B%E8%A8%98%E4%BA%8B" title="Category:数学に関する記事">数学に関する記事</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">隠しカテゴリ: <ul><li><a href="/wiki/Category:Webarchive%E3%83%86%E3%83%B3%E3%83%97%E3%83%AC%E3%83%BC%E3%83%88%E3%81%AE%E3%82%A6%E3%82%A7%E3%82%A4%E3%83%90%E3%83%83%E3%82%AF%E3%83%AA%E3%83%B3%E3%82%AF" title="Category:Webarchiveテンプレートのウェイバックリンク">Webarchiveテンプレートのウェイバックリンク</a></li><li><a href="/wiki/Category:%E6%97%A5%E6%9C%AC%E8%AA%9E%E7%89%88%E8%A8%98%E4%BA%8B%E3%81%8C%E3%83%AA%E3%83%80%E3%82%A4%E3%83%AC%E3%82%AF%E3%83%88%E3%81%AE%E4%BB%AE%E3%83%AA%E3%83%B3%E3%82%AF%E3%82%92%E5%90%AB%E3%82%80%E8%A8%98%E4%BA%8B" title="Category:日本語版記事がリダイレクトの仮リンクを含む記事">日本語版記事がリダイレクトの仮リンクを含む記事</a></li><li><a href="/wiki/Category:%E3%81%99%E3%81%B9%E3%81%A6%E3%81%AE%E3%82%B9%E3%82%BF%E3%83%96%E8%A8%98%E4%BA%8B" title="Category:すべてのスタブ記事">すべてのスタブ記事</a></li><li><a href="/wiki/Category:%E7%89%A9%E7%90%86%E5%AD%A6%E9%96%A2%E9%80%A3%E3%81%AE%E3%82%B9%E3%82%BF%E3%83%96%E9%A0%85%E7%9B%AE" title="Category:物理学関連のスタブ項目">物理学関連のスタブ項目</a></li><li><a href="/wiki/Category:%E6%95%B0%E5%AD%A6%E9%96%A2%E9%80%A3%E3%81%AE%E3%82%B9%E3%82%BF%E3%83%96%E9%A0%85%E7%9B%AE" title="Category:数学関連のスタブ項目">数学関連のスタブ項目</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> 最終更新 2024年8月30日 (金) 13:31 （日時は<a href="/wiki/%E7%89%B9%E5%88%A5:%E5%80%8B%E4%BA%BA%E8%A8%AD%E5%AE%9A#mw-prefsection-rendering" title="特別:個人設定">個人設定</a>で未設定ならば<a href="/wiki/%E5%8D%94%E5%AE%9A%E4%B8%96%E7%95%8C%E6%99%82" title="協定世界時">UTC</a>）。</li> <li id="footer-info-copyright">テキストは<a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.ja">クリエイティブ・コモンズ表示-継承ライセンス</a>のもとで利用できます。追加の条件が適用される場合があります。詳細については<a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">利用規約</a>を参照してください。</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy/ja">プライバシー・ポリシー</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:%E3%82%A6%E3%82%A3%E3%82%AD%E3%83%9A%E3%83%87%E3%82%A3%E3%82%A2%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6">ウィキペディアについて</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:%E5%85%8D%E8%B2%AC%E4%BA%8B%E9%A0%85">免責事項</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">行動規範</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">開発者</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/ja.wikipedia.org">統計</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookieに関する声明</a></li> <li id="footer-places-mobileview"><a href="//ja.m.wikipedia.org/w/index.php?title=%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">モバイルビュー</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-5ccf8d5c58-pjpgz","wgBackendResponseTime":149,"wgPageParseReport":{"limitreport":{"cputime":"0.238","walltime":"0.337","ppvisitednodes":{"value":5857,"limit":1000000},"postexpandincludesize":{"value":50017,"limit":2097152},"templateargumentsize":{"value":10547,"limit":2097152},"expansiondepth":{"value":20,"limit":100},"expensivefunctioncount":{"value":1,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":17502,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 223.129 1 -total"," 46.01% 102.663 6 Template:Citation/core"," 40.99% 91.468 5 Template:Cite_book"," 27.38% 61.096 5 Template:Citation/identifier"," 24.85% 55.450 1 Template:Physics-stub"," 24.84% 55.427 2 Template:Asbox"," 23.07% 51.469 3 Template:ISBN2"," 14.00% 31.231 3 Template:Catalog_lookup_link"," 9.30% 20.753 1 Template:Cite_journal"," 7.95% 17.734 1 Template:Lang-en-short"]},"scribunto":{"limitreport-timeusage":{"value":"0.067","limit":"10.000"},"limitreport-memusage":{"value":1830582,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-7fc47fc68d-pb6p2","timestamp":"20241128183130","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"\u30b9\u30b1\u30fc\u30eb\u56e0\u5b50 (\u5b87\u5b99\u8ad6)","url":"https:\/\/ja.wikipedia.org\/wiki\/%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90_(%E5%AE%87%E5%AE%99%E8%AB%96)","sameAs":"http:\/\/www.wikidata.org\/entity\/Q1332997","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q1332997","author":{"@type":"Organization","name":"\u30a6\u30a3\u30ad\u30e1\u30c7\u30a3\u30a2\u30d7\u30ed\u30b8\u30a7\u30af\u30c8\u3078\u306e\u8ca2\u732e\u8005"},"publisher":{"@type":"Organization","name":"\u30a6\u30a3\u30ad\u30e1\u30c7\u30a3\u30a2\u8ca1\u56e3","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2014-07-04T22:35:01Z","dateModified":"2024-08-30T13:31:01Z","headline":"\u5b87\u5b99\u8ad6"}</script> </body> </html>