Densité critique — Wikipédia

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<a class="vector-toc-link" href="#Formule_donnant_la_densité_critique"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Formule donnant la densité critique</span> </div> </a> <ul id="toc-Formule_donnant_la_densité_critique-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Valeur_actuelle_de_la_densité_critique" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Valeur_actuelle_de_la_densité_critique"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Valeur actuelle de la densité critique</span> </div> </a> <ul id="toc-Valeur_actuelle_de_la_densité_critique-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Paramètres_de_densités" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Paramètres_de_densités"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Paramètres de densités</span> </div> </a> <ul id="toc-Paramètres_de_densités-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Densité_critique_et_devenir_de_l'expansion_de_l'Univers" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Densité_critique_et_devenir_de_l'expansion_de_l'Univers"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Densité critique et devenir de l'expansion de l'Univers</span> </div> </a> <ul id="toc-Densité_critique_et_devenir_de_l'expansion_de_l'Univers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_et_références" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_et_références"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Notes et références</span> </div> </a> <button aria-controls="toc-Notes_et_références-sublist" class="cdx-button cdx-button--weight-quiet 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<span>Afficher / masquer la sous-section Voir aussi</span> </button> <ul id="toc-Voir_aussi-sublist" class="vector-toc-list"> <li id="toc-Bibliographie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliographie"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Bibliographie</span> </div> </a> <ul id="toc-Bibliographie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Article_connexe" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Article_connexe"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Article connexe</span> </div> </a> <ul id="toc-Article_connexe-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liens_externes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liens_externes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Liens externes</span> </div> </a> <ul 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src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/20px-Logo_disambig.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/30px-Logo_disambig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/40px-Logo_disambig.svg.png 2x" data-file-width="512" data-file-height="375" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p>Pour les articles homonymes, voir <a href="/wiki/Densit%C3%A9_(homonymie)" class="mw-disambig" title="Densité (homonymie)">densité (homonymie)</a>. </p> </div></div> <p>En <a href="/wiki/Cosmologie" title="Cosmologie">cosmologie</a>, la <b>densité critique</b> (en <a href="/wiki/Anglais" title="Anglais">anglais</a> : <span class="lang-en" lang="en"><i>critical density</i></span>) ou <b>masse volumique critique</b><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup> est la <a href="/wiki/Densit%C3%A9_d%27%C3%A9nergie" title="Densité d'énergie">densité d'énergie</a>, exprimée en <a href="/wiki/Masse_volumique" title="Masse volumique">masse volumique</a>, pour laquelle l'<a href="/wiki/Espace-temps" title="Espace-temps">espace-temps</a> est plat à grande échelle<sup id="cite_ref-densité_critique_2-0" class="reference"><a href="#cite_note-densité_critique-2"><span class="cite_crochet">[</span>2<span class="cite_crochet">]</span></a></sup>. En d'autres termes, la densité critique d'énergie est la densité d'énergie pour laquelle la <a href="/wiki/Courbure_spatiale" title="Courbure spatiale">courbure spatiale</a> d'un univers <a href="/wiki/Homog%C3%A9n%C3%A9it%C3%A9_(cosmologie)" title="Homogénéité (cosmologie)">homogène</a>, <a href="/wiki/Isotropie_(cosmologie)" title="Isotropie (cosmologie)">isotrope</a> et en <a href="/wiki/Expansion_de_l%27Univers" title="Expansion de l'Univers">expansion</a> est nulle. Si l'on considère un <a href="/wiki/Mod%C3%A8le_cosmologique" title="Modèle cosmologique">modèle cosmologique</a> homogène et isotrope, la densité critique sépare donc, à <a href="/wiki/Taux_d%27expansion_(cosmologie)" title="Taux d'expansion (cosmologie)">taux d'expansion</a> fixé, les modèles dits « fermés » (en fait à courbure spatiale positive) des modèles dit « ouverts » (en fait à courbure spatiale négative). Un univers dont la densité est égale à la densité critique possède une courbure spatiale nulle, c'est-à-dire que les lois de la <a href="/wiki/G%C3%A9om%C3%A9trie_euclidienne" title="Géométrie euclidienne">géométrie euclidienne</a> usuelle sont valables. </p><p>La densité critique est une notion introduite par <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> (<time>1879</time>-<time>1955</time>) et <a href="/wiki/Willem_de_Sitter" title="Willem de Sitter">Willem de Sitter</a> (<time>1872</time>-<time>1934</time>) en <time class="nowrap date-lien" datetime="1932" data-sort-value="1932"><a href="/wiki/1932_en_science" title="1932 en science">1932</a></time><sup id="cite_ref-KraghOverduin201450_3-0" class="reference"><a href="#cite_note-KraghOverduin201450-3"><span class="cite_crochet">[</span>3<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-Einsteinde_Sitter1932_4-0" class="reference"><a href="#cite_note-Einsteinde_Sitter1932-4"><span class="cite_crochet">[</span>4<span class="cite_crochet">]</span></a></sup>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Notation">Notation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=1" title="Modifier la section : Notation" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=1" title="Modifier le code source de la section : Notation"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La densité critique est couramment notée <i>ρ</i><sub>c</sub>, <a href="https://fr.wiktionary.org/wiki/notation" class="extiw" title="wikt:notation">notation</a> composée de la <a href="/wiki/Lettre_(alphabet)" title="Lettre (alphabet)">lettre</a> <a href="/wiki/Alphabet_grec" title="Alphabet grec">grecque</a> <a href="/wiki/Rh%C3%B4" title="Rhô">rhô</a> <a href="/wiki/Bas-de-casse" class="mw-redirect" title="Bas-de-casse">minuscule</a> <a href="/wiki/Italique_(typographie)" title="Italique (typographie)">italique</a>, <a href="/wiki/Symbole" title="Symbole">symbole</a> usuel de la masse volumique<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite_crochet">[</span>5<span class="cite_crochet">]</span></a></sup>, suivie, à droite et en <a href="/wiki/Indice_(typographie)" title="Indice (typographie)">indice</a>, de la lettre <a href="/wiki/Alphabet_latin" title="Alphabet latin">latine</a> <a href="/wiki/C_(lettre)" title="C (lettre)">c</a> minuscule <a href="/wiki/Romain_(typographie)" title="Romain (typographie)">romaine</a>, <a href="/wiki/Initiale_(lettre)" title="Initiale (lettre)">initiale</a> de l'anglais <i><a href="https://fr.wiktionary.org/wiki/critical#Anglais" class="extiw" title="wikt:critical"><span class="lang-en" lang="en">critical</span></a></i> (« <a href="https://fr.wiktionary.org/wiki/critique#Français" class="extiw" title="wikt:critique">critique</a> »). </p> <div class="mw-heading mw-heading2"><h2 id="Formule_donnant_la_densité_critique"><span id="Formule_donnant_la_densit.C3.A9_critique"></span>Formule donnant la densité critique</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=2" title="Modifier la section : Formule donnant la densité critique" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=2" title="Modifier le code source de la section : Formule donnant la densité critique"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Il existe une relation entre taux d'expansion, courbure spatiale et densité d'énergie, donnée par les équations de la <a href="/wiki/Relativit%C3%A9_g%C3%A9n%C3%A9rale" title="Relativité générale">relativité générale</a> appliquées à un modèle d'univers homogène et isotrope. Dans ce contexte, ces équations s'appellent <a href="/wiki/%C3%89quations_de_Friedmann" title="Équations de Friedmann">équations de Friedmann-Lemaître</a>. Elles indiquent que </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 \left({H^{2}}+{\frac {Kc^{2}}{a^{2}}}\right)={\frac {8\pi G}{3c^{2}}}\rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>K</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>8</mn> <mi>π</mi> <mi>G</mi> </mrow> <mrow> <mn>3</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({H^{2}}+{\frac {Kc^{2}}{a^{2}}}\right)={\frac {8\pi G}{3c^{2}}}\rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c875fee9c1f91f9a31b6e47d0513b7a8faeeeb1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.84ex; height:6.343ex;" alt="{\displaystyle \left({H^{2}}+{\frac {Kc^{2}}{a^{2}}}\right)={\frac {8\pi G}{3c^{2}}}\rho }"></span>,</dd></dl> <p>où <i>H</i> est le taux d'expansion (dont la dimension est l'inverse d'un temps), <i>K</i>/<i>a</i><sup>2</sup> la courbure spatiale, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> la densité d'énergie, <i>c</i> la <a href="/wiki/Vitesse_de_la_lumi%C3%A8re" title="Vitesse de la lumière">vitesse de la lumière</a> et <i>G</i> la <a href="/wiki/Constante_de_Newton" class="mw-redirect" title="Constante de Newton">constante universelle de gravitation de Newton</a>. </p><p>La densité critique est mise en évidence à partir de la <a href="/wiki/%C3%89quations_de_Friedmann-Lema%C3%AEtre" class="mw-redirect" title="Équations de Friedmann-Lemaître">première équation de Friedmann-Lemaître</a><sup id="cite_ref-BarrauGrain2023141<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>_6-0" class="reference"><a href="#cite_note-BarrauGrain2023141<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>-6"><span class="cite_crochet">[</span>6<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-Hooper202422<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.7_7-0" class="reference"><a href="#cite_note-Hooper202422<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.7-7"><span class="cite_crochet">[</span>7<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-Taillet2023<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>_8-0" class="reference"><a href="#cite_note-Taillet2023<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>-8"><span class="cite_crochet">[</span>8<span class="cite_crochet">]</span></a></sup>. Celle-ci peut s'écrire<sup id="cite_ref-BarrauGrain2023141_(7.69)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>_9-0" class="reference"><a href="#cite_note-BarrauGrain2023141_(7.69)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>-9"><span class="cite_crochet">[</span>9<span class="cite_crochet">]</span></a></sup> : </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 -kc^{2}=a^{2}H^{2}\left(1-{\frac {8\pi G\rho }{3c^{2}H^{2}}}-{\frac {\Lambda c^{2}}{3c^{2}H^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>k</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>8</mn> <mi>π</mi> <mi>G</mi> <mi>ρ</mi> </mrow> <mrow> <mn>3</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Λ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>3</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -kc^{2}=a^{2}H^{2}\left(1-{\frac {8\pi G\rho }{3c^{2}H^{2}}}-{\frac {\Lambda c^{2}}{3c^{2}H^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c44b106505dd713fae0bd4d1b5d562edf6453278" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:38.707ex; height:6.343ex;" alt="{\displaystyle -kc^{2}=a^{2}H^{2}\left(1-{\frac {8\pi G\rho }{3c^{2}H^{2}}}-{\frac {\Lambda c^{2}}{3c^{2}H^{2}}}\right)}"></span>.</dd></dl> <p>Si <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 k=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6307c8a99dad7d0bcb712352ae0a748bd99a038b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.472ex; height:2.176ex;" alt="{\displaystyle k=0}"></span>, alors<sup id="cite_ref-BarrauGrain2023141_(7.70)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>_10-0" class="reference"><a href="#cite_note-BarrauGrain2023141_(7.70)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>-10"><span class="cite_crochet">[</span>10<span class="cite_crochet">]</span></a></sup> : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {8\pi G\rho }{3c^{2}H^{2}}}+{\frac {\Lambda c^{2}}{3c^{2}H^{2}}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>8</mn> <mi>π</mi> <mi>G</mi> <mi>ρ</mi> </mrow> <mrow> <mn>3</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Λ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>3</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {8\pi G\rho }{3c^{2}H^{2}}}+{\frac {\Lambda c^{2}}{3c^{2}H^{2}}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8d643347a29621fa50dd9915a506948f3302085" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:21.536ex; height:6.009ex;" alt="{\displaystyle {\frac {8\pi G\rho }{3c^{2}H^{2}}}+{\frac {\Lambda c^{2}}{3c^{2}H^{2}}}=1}"></span>.</dd></dl> <p>Si <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 k=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6307c8a99dad7d0bcb712352ae0a748bd99a038b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.472ex; height:2.176ex;" alt="{\displaystyle k=0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Lambda =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf7c27356a14b2aa53072d051b92135d56cbc986" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.874ex; height:2.176ex;" alt="{\displaystyle \Lambda =0}"></span>, alors : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {8\pi G\rho }{3c^{2}H^{2}}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>8</mn> <mi>π</mi> <mi>G</mi> <mi>ρ</mi> </mrow> <mrow> <mn>3</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {8\pi G\rho }{3c^{2}H^{2}}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd9e5039a3b499c7847adb13511c8570673210bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.478ex; height:5.843ex;" alt="{\displaystyle {\frac {8\pi G\rho }{3c^{2}H^{2}}}=1}"></span>,</dd></dl> <p>soit : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho ={\frac {3c^{2}H^{2}}{8\pi G}}=\rho _{\rm {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>8</mn> <mi>π</mi> <mi>G</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {3c^{2}H^{2}}{8\pi G}}=\rho _{\rm {c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1d74ee510c18bddf4cd7590dc221480ff762c02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.78ex; height:5.843ex;" alt="{\displaystyle \rho ={\frac {3c^{2}H^{2}}{8\pi G}}=\rho _{\rm {c}}}"></span>.</dd></dl> <p>La densité critique d'énergie <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\rm {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\rm {c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98ea721ff8fc13a6b4665800fc86bf89f5acd747" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.164ex; height:2.176ex;" alt="{\displaystyle \rho _{\rm {c}}}"></span> est définie comme la densité d'énergie <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> que doit prendre un univers sans <a href="/wiki/Constante_cosmologique" title="Constante cosmologique">constante cosmologique</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(\Lambda =0\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">Λ</mi> <mo>=</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(\Lambda =0\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9f4e888129f7a997faf1ec1ac64ca2f42485127" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.683ex; height:2.843ex;" alt="{\displaystyle \left(\Lambda =0\right)}"></span> pour que sa <a href="/wiki/Courbure_spatiale" title="Courbure spatiale">courbure spatiale</a> soit nulle <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 \left(k=0\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(k=0\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/371c66040ecbce220b1c7f816438f5246e61df7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.281ex; height:2.843ex;" alt="{\displaystyle \left(k=0\right)}"></span><sup id="cite_ref-BarrauGrain2023141<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>_6-1" class="reference"><a href="#cite_note-BarrauGrain2023141<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>-6"><span class="cite_crochet">[</span>6<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-LiddleLyth200017<span_class="nowrap"><abbr_class="abbr_"_title="chapitre(s)"_>chap.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.1,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;2.1.3</span>_11-0" class="reference"><a href="#cite_note-LiddleLyth200017<span_class="nowrap"><abbr_class="abbr_"_title="chapitre(s)"_>chap.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.1,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;2.1.3</span>-11"><span class="cite_crochet">[</span>11<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-Taillet2023279<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>_12-0" class="reference"><a href="#cite_note-Taillet2023279<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>-12"><span class="cite_crochet">[</span>12<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-Wands2014664,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;30.3_13-0" class="reference"><a href="#cite_note-Wands2014664,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;30.3-13"><span class="cite_crochet">[</span>13<span class="cite_crochet">]</span></a></sup>. On a donc<sup id="cite_ref-Adler2021255_(16.10)<span_class="nowrap"><abbr_class="abbr_"_title="chapitre(s)"_>chap.</abbr>&nbsp;16</span>,_<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;16.5_14-0" class="reference"><a href="#cite_note-Adler2021255_(16.10)<span_class="nowrap"><abbr_class="abbr_"_title="chapitre(s)"_>chap.</abbr>&nbsp;16</span>,_<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;16.5-14"><span class="cite_crochet">[</span>14<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-Cianfrani_2014Cianfrani_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_201445_(2.25)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.4,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;2.4.2</span>_15-0" class="reference"><a href="#cite_note-Cianfrani_2014Cianfrani_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_201445_(2.25)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.4,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;2.4.2</span>-15"><span class="cite_crochet">[</span>15<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-Taillet2023279_(4.17)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>_16-0" class="reference"><a href="#cite_note-Taillet2023279_(4.17)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>-16"><span class="cite_crochet">[</span>16<span class="cite_crochet">]</span></a></sup> : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\rm {c}}\equiv {\frac {3c^{2}H^{2}}{8\pi G}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mo>≡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>8</mn> <mi>π</mi> <mi>G</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\rm {c}}\equiv {\frac {3c^{2}H^{2}}{8\pi G}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ec7a6625662bed860bd560bc81593370c4db7fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.48ex; height:5.843ex;" alt="{\displaystyle \rho _{\rm {c}}\equiv {\frac {3c^{2}H^{2}}{8\pi G}}}"></span>.</dd></dl> <p>L'<a href="/wiki/Analyse_dimensionnelle" title="Analyse dimensionnelle">analyse dimensionnelle</a> permet de vérifier que cette formule correspond à une densité d'énergie, dont l'unité dans le <a href="/wiki/Syst%C3%A8me_international_d%27unit%C3%A9s" title="Système international d'unités">Système international</a> est le <a href="/wiki/Joule" title="Joule">joule</a> par <a href="/wiki/M%C3%A8tre_cube" title="Mètre cube">mètre cube</a> <span style="font-size:1.2em; line-height: 1.2em;">(</span><abbr class="abbr" title="par Jm cube">Jm<sup>−3</sup></abbr><span style="font-size:1.2em; line-height: 1.2em;">)</span><sup id="cite_ref-Taillet2023279<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>_12-1" class="reference"><a href="#cite_note-Taillet2023279<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>-12"><span class="cite_crochet">[</span>12<span class="cite_crochet">]</span></a></sup>. </p><p>La densité critique, exprimée en masse volumique, est donnée par<sup id="cite_ref-densité_critique_2-1" class="reference"><a href="#cite_note-densité_critique-2"><span class="cite_crochet">[</span>2<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite_crochet">[</span>17<span class="cite_crochet">]</span></a></sup> : </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 \mu _{\mathrm {c} }={\frac {3H^{2}}{8\pi {G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>8</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{\mathrm {c} }={\frac {3H^{2}}{8\pi {G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43742816f9430010273e3f85cefbae240f7ebdc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.62ex; height:5.843ex;" alt="{\displaystyle \mu _{\mathrm {c} }={\frac {3H^{2}}{8\pi {G}}}}"></span>.</dd></dl> <p>Dans le Système international d'unités, son unité est le <a href="/wiki/Kilogramme_par_m%C3%A8tre_cube" title="Kilogramme par mètre cube">kilogramme par mètre cube</a> (kg/m<sup>3</sup>), l'<a href="/wiki/Unit%C3%A9s_d%C3%A9riv%C3%A9es_du_Syst%C3%A8me_international" class="mw-redirect" title="Unités dérivées du Système international">unité dérivée</a> de masse volumique<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite_crochet">[</span>18<span class="cite_crochet">]</span></a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Valeur_actuelle_de_la_densité_critique"><span id="Valeur_actuelle_de_la_densit.C3.A9_critique"></span>Valeur actuelle de la densité critique</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=3" title="Modifier la section : Valeur actuelle de la densité critique" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=3" title="Modifier le code source de la section : Valeur actuelle de la densité critique"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La densité critique d'énergie est connue dès que le taux d'expansion <i>H</i> l'est. Les mesures les plus précises du taux d'expansion actuel de l'Univers (la <a href="/wiki/Constante_de_Hubble" title="Constante de Hubble">constante de Hubble</a>) donnent<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite_crochet">[</span>19<span class="cite_crochet">]</span></a></sup> </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_{0}=(73\pm 3)\;{\rm {km}}\;{\rm {s}}^{-1}\;{\rm {Mpc}}^{-1}=(2,35\pm 0,10)\times 10^{-18}\;{\rm {s}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>73</mn> <mo>±</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">c</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>35</mn> <mo>±</mo> <mn>0</mn> <mo>,</mo> <mn>10</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>18</mn> </mrow> </msup> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}=(73\pm 3)\;{\rm {km}}\;{\rm {s}}^{-1}\;{\rm {Mpc}}^{-1}=(2,35\pm 0,10)\times 10^{-18}\;{\rm {s}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ef5db4ebf06615d9737cc81904beab85f4c6cfd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:58.363ex; height:3.176ex;" alt="{\displaystyle H_{0}=(73\pm 3)\;{\rm {km}}\;{\rm {s}}^{-1}\;{\rm {Mpc}}^{-1}=(2,35\pm 0,10)\times 10^{-18}\;{\rm {s}}^{-1}}"></span>,</dd> <dd>mais, selon les dernières données (11 septembre 2020) de la mission Planck (<a rel="nofollow" class="external text" href="https://www.aanda.org/articles/aa/full_html/2020/09/aa33910-18/aa33910-18.html"><i>Planck 2018 Results</i>) :</a></dd> <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_{0}=(67,4\pm 0,4)\;{\rm {km}}\;{\rm {s}}^{-1}\;{\rm {Mpc}}^{-1}=(2,18\pm 0,01)\times 10^{-18}\;{\rm {s}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>67</mn> <mo>,</mo> <mn>4</mn> <mo>±</mo> <mn>0</mn> <mo>,</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">c</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>18</mn> <mo>±</mo> <mn>0</mn> <mo>,</mo> <mn>01</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>18</mn> </mrow> </msup> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}=(67,4\pm 0,4)\;{\rm {km}}\;{\rm {s}}^{-1}\;{\rm {Mpc}}^{-1}=(2,18\pm 0,01)\times 10^{-18}\;{\rm {s}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bc9221553eaf013bb9654835f215c2d8db2558b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:62.755ex; height:3.176ex;" alt="{\displaystyle H_{0}=(67,4\pm 0,4)\;{\rm {km}}\;{\rm {s}}^{-1}\;{\rm {Mpc}}^{-1}=(2,18\pm 0,01)\times 10^{-18}\;{\rm {s}}^{-1}}"></span></dd></dl> <p>valeur exprimée, non pas comme de coutume en <a href="/wiki/Kilom%C3%A8tre" title="Kilomètre">kilomètres</a> par seconde et par <a href="/wiki/M%C3%A9gaparsec" class="mw-redirect" title="Mégaparsec">mégaparsec</a>, mais en inverse de seconde (en remarquant que ces deux valeurs restent pour l'instant incompatibles). Injectée dans la formule ci-dessus, cette valeur donne </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\rm {c}}=(9,\!0\pm 0,\!7)\times 10^{-10}\;{\rm {J}}\;{\rm {m}}^{-3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>9</mn> <mo>,</mo> <mspace width="negativethinmathspace" /> <mn>0</mn> <mo>±</mo> <mn>0</mn> <mo>,</mo> <mspace width="negativethinmathspace" /> <mn>7</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>10</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">J</mi> </mrow> </mrow> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\rm {c}}=(9,\!0\pm 0,\!7)\times 10^{-10}\;{\rm {J}}\;{\rm {m}}^{-3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6098b43c1a5ec802fba32cf59765ee591c918902" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.93ex; height:3.176ex;" alt="{\displaystyle \rho _{\rm {c}}=(9,\!0\pm 0,\!7)\times 10^{-10}\;{\rm {J}}\;{\rm {m}}^{-3}}"></span>, mais aussi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\rm {c}}=(7,648\pm 0,\!091)\times 10^{-10}\;{\rm {J}}\;{\rm {m}}^{-3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>7</mn> <mo>,</mo> <mn>648</mn> <mo>±</mo> <mn>0</mn> <mo>,</mo> <mspace width="negativethinmathspace" /> <mn>091</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>10</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">J</mi> </mrow> </mrow> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\rm {c}}=(7,648\pm 0,\!091)\times 10^{-10}\;{\rm {J}}\;{\rm {m}}^{-3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15cebcc618c5287f543e47641089d869d3c05e6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.967ex; height:3.176ex;" alt="{\displaystyle \rho _{\rm {c}}=(7,648\pm 0,\!091)\times 10^{-10}\;{\rm {J}}\;{\rm {m}}^{-3}}"></span>.</dd></dl> <p>Cet ordre de grandeur, peu éclairant, peut être ré-exprimé en termes de <a href="/wiki/Masse_volumique" title="Masse volumique">masse volumique</a> critique ou de densité massique critique, notée aussi <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 \mu _{\rm {c}}=10^{-26}\;{\rm {kg}}\;{\rm {m}}^{-3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>26</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </mrow> </mrow> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{\rm {c}}=10^{-26}\;{\rm {kg}}\;{\rm {m}}^{-3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61f52cd5f519ae12cb5c2489fcbe4cdff134ef25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.891ex; height:3.176ex;" alt="{\displaystyle \mu _{\rm {c}}=10^{-26}\;{\rm {kg}}\;{\rm {m}}^{-3}}"></span>mais aussi<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 \ 8,510\times 10^{-27}\;{\rm {kg}}\;{\rm {m}}^{-3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>8</mn> <mo>,</mo> <mn>510</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>27</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </mrow> </mrow> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 8,510\times 10^{-27}\;{\rm {kg}}\;{\rm {m}}^{-3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5afe30951a8996ebb2a4d720d0bbb879c4ebf66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.533ex; height:3.009ex;" alt="{\displaystyle \ 8,510\times 10^{-27}\;{\rm {kg}}\;{\rm {m}}^{-3}}"></span>, au lieu de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\rm {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\rm {c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98ea721ff8fc13a6b4665800fc86bf89f5acd747" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.164ex; height:2.176ex;" alt="{\displaystyle \rho _{\rm {c}}}"></span>, pour éviter la confusion entre les deux grandeurs critiques, en divisant la densité critique d'énergie par le carré de la vitesse de la lumière, puis en densité critique de <a href="/wiki/Nucl%C3%A9on" title="Nucléon">nucléons</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{\rm {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{\rm {c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/900dff9b9ecb4c422f82d852de2ca45da982e12f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.357ex; height:2.009ex;" alt="{\displaystyle n_{\rm {c}}}"></span> en divisant par la <a href="/wiki/Masse" title="Masse">masse</a> du <a href="/wiki/Proton" title="Proton">proton</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{\rm {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\rm {p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/231d33114af4df9cc70d5fd569bb73b92f874054" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.187ex; height:2.343ex;" alt="{\displaystyle m_{\rm {p}}}"></span>. On obtient alors </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 n_{\rm {c}}={\frac {\rho _{\rm {c}}}{m_{\rm {p}}c^{2}}}={\frac {\mu _{\rm {c}}}{m_{\rm {p}}}}=(6,\!0\pm 0,\!5)\;{\rm {m}}^{-3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mn>6</mn> <mo>,</mo> <mspace width="negativethinmathspace" /> <mn>0</mn> <mo>±</mo> <mn>0</mn> <mo>,</mo> <mspace width="negativethinmathspace" /> <mn>5</mn> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{\rm {c}}={\frac {\rho _{\rm {c}}}{m_{\rm {p}}c^{2}}}={\frac {\mu _{\rm {c}}}{m_{\rm {p}}}}=(6,\!0\pm 0,\!5)\;{\rm {m}}^{-3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86801949fab532f5bff38eb23e1e6a9a2601617f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:37.266ex; height:5.676ex;" alt="{\displaystyle n_{\rm {c}}={\frac {\rho _{\rm {c}}}{m_{\rm {p}}c^{2}}}={\frac {\mu _{\rm {c}}}{m_{\rm {p}}}}=(6,\!0\pm 0,\!5)\;{\rm {m}}^{-3}}"></span>.</dd></dl> <p>La densité massique critique correspond donc à une densité de quelques atomes par mètre cube. Les mesures des <a href="/wiki/Param%C3%A8tre_cosmologique" title="Paramètre cosmologique">paramètres cosmologiques</a> indiquent de plus que la courbure spatiale de l'<a href="/wiki/Univers_observable" title="Univers observable">Univers observable</a> est très faible, c'est-à-dire que sa densité actuelle est très proche de sa densité critique (à quelques pourcents près, voir <a href="/wiki/Mod%C3%A8le_standard_de_la_cosmologie" title="Modèle standard de la cosmologie">modèle standard de la cosmologie</a>). La densité moyenne de l'Univers observable est donc très faible. En fait, la densité d'atomes, essentiellement de l'<a href="/wiki/Hydrog%C3%A8ne" title="Hydrogène">hydrogène</a> et de l'<a href="/wiki/H%C3%A9lium" title="Hélium">hélium</a> (on parle de <a href="/w/index.php?title=Densit%C3%A9_baryonique&action=edit&redlink=1" class="new" title="Densité baryonique (page inexistante)">densité baryonique</a>), est même plus faible que cela, car les mesures actuelles indiquent que seule 5 % de la densité totale de l'Univers est sous forme de <a href="/wiki/Mati%C3%A8re_baryonique" title="Matière baryonique">matière baryonique</a>, soit moins d'un atome par mètre cube. </p> <div class="mw-heading mw-heading2"><h2 id="Paramètres_de_densités"><span id="Param.C3.A8tres_de_densit.C3.A9s"></span>Paramètres de densités</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=4" title="Modifier la section : Paramètres de densités" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=4" title="Modifier le code source de la section : Paramètres de densités"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/Param%C3%A8tre_de_densit%C3%A9" title="Paramètre de densité">Paramètre de densité</a>.</div></div> <p>La densité critique d'énergie introduit naturellement une échelle caractéristique dans les densités d'énergie. Il est souvent commode d'exprimer ces dernières en fonction de celle-là. Ainsi, plutôt que de parler de la densité d'énergie de la matière baryonique, on préfère souvent parler de son <a href="/wiki/Param%C3%A8tre_de_densit%C3%A9" title="Paramètre de densité">paramètre de densité</a>, défini comme étant le rapport de la densité d'énergie correspondant à la densité critique d'énergie. Ce paramètre est noté avec la lettre grecque <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 \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Omega }"></span> et est donc défini par </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 \Omega \equiv {\frac {\rho }{\rho _{\rm {c}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> <mo>≡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega \equiv {\frac {\rho }{\rho _{\rm {c}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a2c47a6a5573371f98d69a12342acaf36f975cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:7.777ex; height:5.343ex;" alt="{\displaystyle \Omega \equiv {\frac {\rho }{\rho _{\rm {c}}}}}"></span>.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Densité_critique_et_devenir_de_l'expansion_de_l'Univers"><span id="Densit.C3.A9_critique_et_devenir_de_l.27expansion_de_l.27Univers"></span>Densité critique et devenir de l'expansion de l'Univers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=5" title="Modifier la section : Densité critique et devenir de l'expansion de l'Univers" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=5" title="Modifier le code source de la section : Densité critique et devenir de l'expansion de l'Univers"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/Destin_de_l%27Univers" title="Destin de l'Univers">Destin de l'Univers</a>.</div></div> <p>Il est parfois indiqué que la valeur de la densité d'énergie par rapport à la densité critique d'énergie détermine le destin de l'expansion de l'Univers. Cette affirmation est en général <b>fausse</b> : il n'y a pas de relation directe entre les valeurs relatives (entre densité d'énergie et densité critique d'énergie), et l'issue de l'expansion de l'Univers. Par exemple, un <a href="/wiki/Univers_de_de_Sitter" title="Univers de de Sitter">univers de de Sitter</a> peut avoir une densité d'énergie supérieure, inférieure ou égale à la densité critique d'énergie, sans que cela modifie le futur de son expansion (qui sera éternelle et tendra vers un taux d'expansion constant). </p><p>Par contre, dans le cas particulier où les seules formes d'énergie sont du <a href="/wiki/Rayonnement_%C3%A9lectromagn%C3%A9tique" title="Rayonnement électromagnétique">rayonnement</a> et de la <a href="/wiki/Mati%C3%A8re_baryonique" title="Matière baryonique">matière baryonique</a> (ou éventuellement de la <a href="/wiki/Mati%C3%A8re_noire" title="Matière noire">matière noire</a>), alors la différence entre densité d'énergie et densité critique d'énergie détermine le devenir de l'expansion. Si cet écart est négatif ou nul, l'expansion se poursuit indéfiniment, s'il est positif, alors l'expansion s'arrêtera pour laisser place à une phase de contraction (<a href="/wiki/Big_Crunch" title="Big Crunch">Big Crunch</a>). </p> <div class="mw-heading mw-heading2"><h2 id="Notes_et_références"><span id="Notes_et_r.C3.A9f.C3.A9rences"></span>Notes et références</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=6" title="Modifier la section : Notes et références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=6" title="Modifier le code source de la section : Notes et références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink noprint"><a href="#cite_ref-1">↑</a> </span><span class="reference-text"><span class="ouvrage" id="Pérez_(dir.)2008"><span class="ouvrage" id="José-Philippe_Pérez_(dir.)2008">José-Philippe <span class="nom_auteur">Pérez (dir.)</span> <i><abbr class="abbr" title="et alii (et d’autres)">et al.</abbr></i>, <cite class="italique">Physique, une introduction</cite>, Bruxelles, De Boeck Université, <time class="nowrap" datetime="2008-02" data-sort-value="2008-02">février 2008</time>, XII-492 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-8041-5573-5" title="Spécial:Ouvrages de référence/978-2-8041-5573-5"><span class="nowrap">978-2-8041-5573-5</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/470905995">470905995</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb41139171c.public">41139171</a></span>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Q19PWa2q6C0C&printsec=frontcover">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physique%2C+une+introduction&rft.place=Bruxelles&rft.pub=De+Boeck+Universit%C3%A9&rft.aulast=P%C3%A9rez+%28dir.%29&rft.aufirst=Jos%C3%A9-Philippe&rft.date=2008-02&rft.tpages=XII-492&rft.isbn=978-2-8041-5573-5&rft_id=info%3Aoclcnum%2F470905995&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>, <abbr class="abbr" title="page">p.</abbr> 107 <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=Q19PWa2q6C0C&pg=RA2-PT107#v=onepage&q&f=false">lire en ligne</a> <abbr class="abbr indicateur-format format-html" title="Fichier au format Hypertext Markup Language (HTML)">[html]</abbr> (consulté le 27 octobre 2014)</span> </li> <li id="cite_note-densité_critique-2"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-densité_critique_2-0">a</a> et <a href="#cite_ref-densité_critique_2-1">b</a></sup> </span><span class="reference-text">Entrée « densité critique », dans <span class="ouvrage" id="TailletFebvreVillain2009"><span class="ouvrage" id="Richard_TailletPascal_FebvreLoïc_Villain2009">Richard <span class="nom_auteur">Taillet</span>, Pascal <span class="nom_auteur">Febvre</span> et Loïc <span class="nom_auteur">Villain</span>, <cite class="italique">Dictionnaire de physique</cite>, Bruxelles, <a href="/wiki/De_Boeck_Universit%C3%A9" class="mw-redirect" title="De Boeck Université">De Boeck Université</a>, 2009 (<abbr class="abbr" title="deuxième">2<sup>e</sup></abbr> éd.) (<abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr> mai 2008), XII-741 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-8041-0248-7" title="Spécial:Ouvrages de référence/978-2-8041-0248-7"><span class="nowrap">978-2-8041-0248-7</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/632092205">632092205</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb421229458.public">42122945</a></span>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dictionnaire+de+physique&rft.place=Bruxelles&rft.pub=De+Boeck+Universit%C3%A9&rft.aulast=Taillet&rft.aufirst=Richard&rft.au=Febvre%2C+Pascal&rft.au=Villain%2C+Lo%C3%AFc&rft.date=2009-11&rft.tpages=XII-741&rft.isbn=978-2-8041-0248-7&rft_id=info%3Aoclcnum%2F632092205&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>, <abbr class="abbr" title="page">p.</abbr> 144 <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=fts1ydufciQC&pg=PA144#v=onepage&q&f=false">lire en ligne</a> <abbr class="abbr indicateur-format format-html" title="Fichier au format Hypertext Markup Language (HTML)">[html]</abbr> (consulté le 27 octobre 2014)</span> </li> <li id="cite_note-KraghOverduin201450-3"><span class="mw-cite-backlink noprint"><a href="#cite_ref-KraghOverduin201450_3-0">↑</a> </span><span class="reference-text"><a href="#KraghOverduin2014">Kragh et Overduin 2014</a>, <abbr class="abbr" title="page(s)">p.</abbr> 50. </span> </li> <li id="cite_note-Einsteinde_Sitter1932-4"><span class="mw-cite-backlink noprint"><a href="#cite_ref-Einsteinde_Sitter1932_4-0">↑</a> </span><span class="reference-text"><a href="#Einsteinde_Sitter1932">Einstein et de Sitter 1932</a>. </span> </li> <li id="cite_note-5"><span class="mw-cite-backlink noprint"><a href="#cite_ref-5">↑</a> </span><span class="reference-text">Entrée « masse volumique », dans <span class="ouvrage" id="TailletFebvreVillain2008"><span class="ouvrage" id="Richard_TailletPascal_FebvreLoïc_Villain2008">Richard <span class="nom_auteur">Taillet</span>, Pascal <span class="nom_auteur">Febvre</span> et Loïc <span class="nom_auteur">Villain</span>, <cite class="italique">Op. cit.</cite>, Bruxelles, De Boeck Université, 2008 (<abbr class="abbr" title="première">1<sup>re</sup></abbr> éd.), XI-672 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-8041-5688-6" title="Spécial:Ouvrages de référence/978-2-8041-5688-6"><span class="nowrap">978-2-8041-5688-6</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/300277324">300277324</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb41256105f.public">41256105</a></span>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Op.+cit.&rft.place=Bruxelles&rft.pub=De+Boeck+Universit%C3%A9&rft.aulast=Taillet&rft.aufirst=Richard&rft.au=Febvre%2C+Pascal&rft.au=Villain%2C+Lo%C3%AFc&rft.date=2008-05&rft.tpages=XI-672&rft.isbn=978-2-8041-5688-6&rft_id=info%3Aoclcnum%2F300277324&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>, <abbr class="abbr" title="page">p.</abbr> 306 <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=wzy4-Jjo2KUC&pg=PA306#v=onepage&q&f=false">lire en ligne</a> <abbr class="abbr indicateur-format format-html" title="Fichier au format Hypertext Markup Language (HTML)">[html]</abbr> (consulté le 27 octobre 2014)</span> </li> <li id="cite_note-BarrauGrain2023141<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>-6"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-BarrauGrain2023141<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>_6-0">a</a> et <a href="#cite_ref-BarrauGrain2023141<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>_6-1">b</a></sup> </span><span class="reference-text"><a href="#BarrauGrain2023">Barrau et Grain 2023</a>, <abbr class="abbr" title="section">sec.</abbr> 7.3, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 7.3.1</span>, <abbr class="abbr" title="page(s)">p.</abbr> 141. </span> </li> <li id="cite_note-Hooper202422<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.7-7"><span class="mw-cite-backlink noprint"><a href="#cite_ref-Hooper202422<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.7_7-0">↑</a> </span><span class="reference-text"><a href="#Hooper2024">Hooper 2024</a>, <abbr class="abbr" title="section">sec.</abbr> 2.7, <abbr class="abbr" title="page(s)">p.</abbr> 22. </span> </li> <li id="cite_note-Taillet2023<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>-8"><span class="mw-cite-backlink noprint"><a href="#cite_ref-Taillet2023<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>_8-0">↑</a> </span><span class="reference-text"><a href="#Taillet2023">Taillet 2023</a>, <abbr class="abbr" title="section">sec.</abbr> 4.3, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 4.3.3</span>. </span> </li> <li id="cite_note-BarrauGrain2023141_(7.69)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>-9"><span class="mw-cite-backlink noprint"><a href="#cite_ref-BarrauGrain2023141_(7.69)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>_9-0">↑</a> </span><span class="reference-text"><a href="#BarrauGrain2023">Barrau et Grain 2023</a>, <abbr class="abbr" title="section">sec.</abbr> 7.3, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 7.3.1</span>, <abbr class="abbr" title="page(s)">p.</abbr> 141 (7.69). </span> </li> <li id="cite_note-BarrauGrain2023141_(7.70)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>-10"><span class="mw-cite-backlink noprint"><a href="#cite_ref-BarrauGrain2023141_(7.70)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;7.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;7.3.1</span>_10-0">↑</a> </span><span class="reference-text"><a href="#BarrauGrain2023">Barrau et Grain 2023</a>, <abbr class="abbr" title="section">sec.</abbr> 7.3, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 7.3.1</span>, <abbr class="abbr" title="page(s)">p.</abbr> 141 (7.70). </span> </li> <li id="cite_note-LiddleLyth200017<span_class="nowrap"><abbr_class="abbr_"_title="chapitre(s)"_>chap.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.1,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;2.1.3</span>-11"><span class="mw-cite-backlink noprint"><a href="#cite_ref-LiddleLyth200017<span_class="nowrap"><abbr_class="abbr_"_title="chapitre(s)"_>chap.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.1,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;2.1.3</span>_11-0">↑</a> </span><span class="reference-text"><a href="#LiddleLyth2000">Liddle et Lyth 2000</a>, <span class="nowrap"><abbr class="abbr" title="chapitre(s)">chap.</abbr> 2</span>, <abbr class="abbr" title="section">sec.</abbr> 2.1, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 2.1.3</span>, <abbr class="abbr" title="page(s)">p.</abbr> 17. </span> </li> <li id="cite_note-Taillet2023279<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>-12"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-Taillet2023279<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>_12-0">a</a> et <a href="#cite_ref-Taillet2023279<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>_12-1">b</a></sup> </span><span class="reference-text"><a href="#Taillet2023">Taillet 2023</a>, <abbr class="abbr" title="section">sec.</abbr> 4.3, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 4.3.3</span>, <abbr class="abbr" title="page(s)">p.</abbr> 279. </span> </li> <li id="cite_note-Wands2014664,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;30.3-13"><span class="mw-cite-backlink noprint"><a href="#cite_ref-Wands2014664,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;30.3_13-0">↑</a> </span><span class="reference-text"><a href="#Wands2014">Wands 2014</a>, <abbr class="abbr" title="section">sec.</abbr> 30.3, <abbr class="abbr" title="page(s)">p.</abbr> 664, <span class="nowrap"><abbr class="abbr" title="colonne(s)">col.</abbr> 1</span>. </span> </li> <li id="cite_note-Adler2021255_(16.10)<span_class="nowrap"><abbr_class="abbr_"_title="chapitre(s)"_>chap.</abbr>&nbsp;16</span>,_<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;16.5-14"><span class="mw-cite-backlink noprint"><a href="#cite_ref-Adler2021255_(16.10)<span_class="nowrap"><abbr_class="abbr_"_title="chapitre(s)"_>chap.</abbr>&nbsp;16</span>,_<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;16.5_14-0">↑</a> </span><span class="reference-text"><a href="#Adler2021">Adler 2021</a>, <span class="nowrap"><abbr class="abbr" title="chapitre(s)">chap.</abbr> 16</span>, <abbr class="abbr" title="section">sec.</abbr> 16.5, <abbr class="abbr" title="page(s)">p.</abbr> 255 (16.10). </span> </li> <li id="cite_note-Cianfrani_2014Cianfrani_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_201445_(2.25)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.4,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;2.4.2</span>-15"><span class="mw-cite-backlink noprint"><a href="#cite_ref-Cianfrani_2014Cianfrani_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_201445_(2.25)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;2.4,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;2.4.2</span>_15-0">↑</a> </span><span class="reference-text"><a href="#Cianfrani_2014">Cianfrani <i><abbr class="abbr" title="et alii (« et d’autres »)" lang="la">et al.</abbr></i> 2014</a>, <abbr class="abbr" title="section">sec.</abbr> 2.4, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 2.4.2</span>, <abbr class="abbr" title="page(s)">p.</abbr> 45 (2.25). </span> </li> <li id="cite_note-Taillet2023279_(4.17)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>-16"><span class="mw-cite-backlink noprint"><a href="#cite_ref-Taillet2023279_(4.17)<abbr_class="abbr_"_title="section"_>sec.</abbr>&nbsp;4.3,_<span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;4.3.3</span>_16-0">↑</a> </span><span class="reference-text"><a href="#Taillet2023">Taillet 2023</a>, <abbr class="abbr" title="section">sec.</abbr> 4.3, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 4.3.3</span>, <abbr class="abbr" title="page(s)">p.</abbr> 279 (4.17). </span> </li> <li id="cite_note-17"><span class="mw-cite-backlink noprint"><a href="#cite_ref-17">↑</a> </span><span class="reference-text"><span class="ouvrage" id="HobsonEfstathiouLasenby2009"><span class="ouvrage" id="Michael_P._HobsonGeorge_EfstathiouAnthony_N._Lasenby2009">Michael P. <span class="nom_auteur">Hobson</span>, <a href="/wiki/George_Efstathiou" title="George Efstathiou">George Efstathiou</a> et Anthony N. <span class="nom_auteur">Lasenby</span> (<abbr class="abbr" title="traduction">trad.</abbr> de l'anglais, traduit de l'anglais par Loïc Villain et révisé par Richard Taillet), <cite class="italique">Relativité générale</cite>, Bruxelles, De Boeck Université, <time class="nowrap" datetime="2009-12" data-sort-value="2009-12">décembre 2009</time>, XX-554 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-8041-0126-8" title="Spécial:Ouvrages de référence/978-2-8041-0126-8"><span class="nowrap">978-2-8041-0126-8</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/664330193">664330193</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb421421742.public">42142174</a></span>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=WUwpAwAAQBAJ&printsec=frontcover">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Relativit%C3%A9+g%C3%A9n%C3%A9rale&rft.place=Bruxelles&rft.pub=De+Boeck+Universit%C3%A9&rft.aulast=Hobson&rft.aufirst=Michael+P.&rft.au=George+Efstathiou&rft.au=Lasenby%2C+Anthony+N.&rft.date=2009-12&rft.tpages=XX-554&rft.isbn=978-2-8041-0126-8&rft_id=info%3Aoclcnum%2F664330193&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>, <abbr class="abbr" title="page">p.</abbr> 387 <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=0EDTUmS9ShYC&pg=PA387#v=onepage&q&f=false">lire en ligne</a> <abbr class="abbr indicateur-format format-html" title="Fichier au format Hypertext Markup Language (HTML)">[html]</abbr> (consulté le 27 octobre 2014)</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink noprint"><a href="#cite_ref-18">↑</a> </span><span class="reference-text">Entrées « kilogramme par mètre cube » et « masse volumique », dans <span class="ouvrage" id="Dubesset2000"><span class="ouvrage" id="Michel_Dubesset2000">Michel <span class="nom_auteur">Dubesset</span> (préf. de Gérard Grau), <cite class="italique">Le manuel du Système international d'unités : lexique et conversions</cite>, Paris, Technip, <abbr class="abbr" title="collection">coll.</abbr> « Publications de l'Institut français du pétrole », <time>2000</time>, 169 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/2-7108-0762-9" title="Spécial:Ouvrages de référence/2-7108-0762-9"><span class="nowrap">2-7108-0762-9</span></a>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb37624276j.public">37624276</a></span>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6_rdRIKf67gC&printsec=frontcover">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Le+manuel+du+Syst%C3%A8me+international+d%27unit%C3%A9s&rft.place=Paris&rft.pub=Technip&rft.stitle=lexique+et+conversions&rft.aulast=Dubesset&rft.aufirst=Michel&rft.date=2000&rft.tpages=169&rft.isbn=2-7108-0762-9&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>, <abbr class="abbr" title="page">p.</abbr> 81 <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=6_rdRIKf67gC&pg=PA81#v=onepage&q&f=false">lire en ligne</a> <abbr class="abbr indicateur-format format-html" title="Fichier au format Hypertext Markup Language (HTML)">[html]</abbr> (consulté le 27 octobre 2014) et <abbr class="abbr" title="page">p.</abbr> 86 <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=6_rdRIKf67gC&pg=PA86#v=onepage&q&f=false">lire en ligne</a> <abbr class="abbr indicateur-format format-html" title="Fichier au format Hypertext Markup Language (HTML)">[html]</abbr> (consulté le 27 octobre 2014)</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink noprint"><a href="#cite_ref-19">↑</a> </span><span class="reference-text">Voir par exemple les derniers résultats de la <a href="/wiki/Satellite_artificiel" title="Satellite artificiel">sonde spatiale</a> <a href="/wiki/WMAP" class="mw-redirect" title="WMAP">WMAP</a>, <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> <a href="/wiki/David_Nathaniel_Spergel" class="mw-redirect" title="David Nathaniel Spergel">David Nathaniel Spergel</a> <i>et al.</i>, « <i>Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology</i> », soumis à <i><a href="/wiki/The_Astrophysical_Journal" title="The Astrophysical Journal">The Astrophysical Journal</a></i> (<a rel="nofollow" class="external text" href="http://fr.arxiv.org/abs/astro-ph/0603449">voir en ligne</a>)</span> </li> </ol> </div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=7" title="Modifier la section : Sources" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=7" title="Modifier le code source de la section : Sources"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Voir <a href="/wiki/Portail:Cosmologie/Ouvrages_sp%C3%A9cialis%C3%A9s_sur_la_cosmologie" title="Portail:Cosmologie/Ouvrages spécialisés sur la cosmologie">Ouvrages spécialisés sur la cosmologie</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voir_aussi">Voir aussi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=8" title="Modifier la section : Voir aussi" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=8" title="Modifier le code source de la section : Voir aussi"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Bibliographie">Bibliographie</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=9" title="Modifier la section : Bibliographie" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=9" title="Modifier le code source de la section : Bibliographie"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="ouvrage" id="Adler2021"><span class="ouvrage" id="Ronald_J._Adler2021"><small>[Adler 2021]</small> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Ronald J. <span class="nom_auteur">Adler</span>, <cite class="italique" lang="en">General relativity and cosmology : a first encounter</cite>, Cham, <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>, <abbr class="abbr" title="collection">coll.</abbr> « Graduate texts in physics », <time class="nowrap" datetime="2021-01" data-sort-value="2021-01">janvier 2021</time>, <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="14"><span class="romain" style="text-transform:uppercase">XIV</span></abbr>-313 <abbr class="abbr" title="pages">p.</abbr>, 15,9 × 23,5 <abbr class="abbr" title="centimètre">cm</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-3-030-61573-4" title="Spécial:Ouvrages de référence/978-3-030-61573-4"><span class="nowrap">978-3-030-61573-4</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9783030615734" title="Spécial:Ouvrages de référence/9783030615734"><span class="nowrap">9783030615734</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/1314056327">1314056327</a></span>, <a href="/wiki/Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007/978-3-030-61574-1">10.1007/978-3-030-61574-1</a></span>, <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021grc..book.....A">2021grc..book.....A</a></span>, <a href="/wiki/Semantic_Scholar" title="Semantic Scholar">S2CID</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:241866887">241866887</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/262214423">262214423</a></span>, <a rel="nofollow" class="external text" href="https://link.springer.com/book/10.1007/978-3-030-61574-1">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=Y8UWEAAAQBAJ">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=General+relativity+and+cosmology&rft.place=Cham&rft.pub=Springer&rft.edition=1&rft.stitle=a+first+encounter&rft.aulast=Adler&rft.aufirst=Ronald+J.&rft.date=2021-01&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%2214%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EXIV%3C%2Fspan%3E%3C%2Fabbr%3E-313&rft.isbn=978-3-030-61573-4&rft_id=info%3Adoi%2F10.1007%2F978-3-030-61574-1&rft_id=info%3Aoclcnum%2F1314056327&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>.</li> <li><span class="ouvrage" id="BarrauGrain2023"><span class="ouvrage" id="Aurélien_BarrauJulien_Grain2023"><small>[Barrau et Grain 2023]</small> <a href="/wiki/Aur%C3%A9lien_Barrau" title="Aurélien Barrau">Aurélien <span class="nom_auteur">Barrau</span></a> et Julien <span class="nom_auteur">Grain</span>, <cite class="italique">Relativité générale : cours et exercices corrigés</cite>, Malakoff, <a href="/wiki/%C3%89ditions_Dunod" title="Éditions Dunod">Dunod</a>, <abbr class="abbr" title="collection">coll.</abbr> « Science sup / physique », <time class="nowrap" datetime="2023-08" data-sort-value="2023-08">août 2023</time>, <abbr class="abbr" title="troisième">3<sup>e</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr> (<abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr> <time class="nowrap" datetime="2011-08" data-sort-value="2011-08">août 2011</time>), <abbr class="abbr" title="5"><span class="romain" style="text-transform:uppercase">V</span></abbr>-248 <abbr class="abbr" title="pages">p.</abbr>, 17 × 24 <abbr class="abbr" title="centimètre">cm</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-10-084799-0" title="Spécial:Ouvrages de référence/978-2-10-084799-0"><span class="nowrap">978-2-10-084799-0</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9782100847990" title="Spécial:Ouvrages de référence/9782100847990"><span class="nowrap">9782100847990</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/1395956819">1395956819</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb47313122g.public">47313122</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/271703571">271703571</a></span>, <a rel="nofollow" class="external text" href="https://www.dunod.com/sciences-techniques/relativite-generale-cours-et-exercices-corriges-1">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=NKXNEAAAQBAJ">lire en ligne</a>)</small>, <abbr class="abbr" title="chapitre(s)">chap.</abbr> 7 (« Cosmologie »), <abbr class="abbr" title="pages">p.</abbr> <span class="nowrap">127-178</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Relativit%C3%A9+g%C3%A9n%C3%A9rale&rft.atitle=Cosmologie&rft.place=Malakoff&rft.pub=Dunod&rft.edition=3&rft.stitle=cours+et+exercices+corrig%C3%A9s&rft.aulast=Barrau&rft.aufirst=Aur%C3%A9lien&rft.au=Grain%2C+Julien&rft.date=2023-08&rft.pages=127-178&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%225%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EV%3C%2Fspan%3E%3C%2Fabbr%3E-248&rft.isbn=978-2-10-084799-0&rft_id=info%3Aoclcnum%2F1395956819&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>.</li> <li><span class="ouvrage" id="Cianfrani_2014"><small>[Cianfrani <i><abbr class="abbr" title="et alii (« et d’autres »)" lang="la">et al.</abbr></i> 2014]</small> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Francesco <span class="nom_auteur">Cianfrani</span>, Orchidea Maria <span class="nom_auteur">Lecian</span>, Matteo <span class="nom_auteur">Lulli</span> et Giovanni <span class="nom_auteur">Montani</span>, <cite class="italique" lang="en">Canonical quantum gravity : fundamentals and recent developments</cite>, Singapour, <a href="/wiki/World_Scientific" title="World Scientific">World Scientific</a>, hors <abbr class="abbr" title="collection">coll.</abbr>, <time class="nowrap" datetime="2014-04" data-sort-value="2014-04">avril 2014</time>, <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="23"><span class="romain" style="text-transform:uppercase">XXIII</span></abbr>-299 <abbr class="abbr" title="pages">p.</abbr>, 15,2 × 22,9 <abbr class="abbr" title="centimètre">cm</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-981-4556-64-4" title="Spécial:Ouvrages de référence/978-981-4556-64-4"><span class="nowrap">978-981-4556-64-4</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9789814556644" title="Spécial:Ouvrages de référence/9789814556644"><span class="nowrap">9789814556644</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/935653730">935653730</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb44280309z.public">44280309</a></span>, <a href="/wiki/Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1142/8957">10.1142/8957</a></span>, <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014cqgf.book.....C">2014cqgf.book.....C</a></span>, <a href="/wiki/Semantic_Scholar" title="Semantic Scholar">S2CID</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118872619">118872619</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/190874333">190874333</a></span>, <a rel="nofollow" class="external text" href="https://www.worldscientific.com/worldscibooks/10.1142/8957">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=7kW7CgAAQBAJ">lire en ligne</a>)</small>, <span class="nowrap"><abbr class="abbr" title="chapitre(s)">chap.</abbr> 2</span> (« Elements of cosmology »), <abbr class="abbr" title="pages">p.</abbr> <span class="nowrap">31-56</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Canonical+quantum+gravity&rft.place=Singapour&rft.pub=World+Scientific&rft.edition=1&rft.stitle=fundamentals+and+recent+developments&rft.aulast=Cianfrani&rft.aufirst=Francesco&rft.au=Lecian%2C+Orchidea+Maria&rft.au=Lulli%2C+Matteo&rft.au=Montani%2C+Giovanni&rft.date=2014&rft.pages=31-56&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%2223%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EXXIII%3C%2Fspan%3E%3C%2Fabbr%3E-299&rft.isbn=978-981-4556-64-4&rft_id=info%3Adoi%2F10.1142%2F8957&rft_id=info%3Aoclcnum%2F935653730&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span>.</li> <li><span class="ouvrage" id="Einsteinde_Sitter1932"><span class="ouvrage" id="Albert_EinsteinWillem_de_Sitter1932"><small>[Einstein et de Sitter 1932]</small> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert <span class="nom_auteur">Einstein</span></a> et <a href="/wiki/Willem_de_Sitter" title="Willem de Sitter">Willem <span class="nom_auteur">de Sitter</span></a>, « <cite style="font-style:normal" lang="en">On the relation between the expansion and the mean density of the Universe</cite> », <i><span class="lang-en" lang="en"><a href="/wiki/Proceedings_of_the_National_Academy_of_Sciences" title="Proceedings of the National Academy of Sciences">PNAS</a></span></i>, <abbr class="abbr" title="volume">vol.</abbr> 18, <abbr class="abbr" title="numéro">n<sup>o</sup></abbr> 3,‎ <time class="nowrap" datetime="1932-03-15" data-sort-value="1932-03-15">15 mars 1932</time> <small style="line-height:1em;">(<a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/9985762814">9985762814</a></span>, <a href="/wiki/PubMed" title="PubMed">PMID</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pubmed/16587663">16587663</a></span>, <a href="/wiki/PubMed_Central" title="PubMed Central">PMCID</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1076193">PMC1076193</a></span>, <a href="/wiki/Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1073/pnas.18.3.213">10.1073/pnas.18.3.213</a></span>, <a href="/wiki/JSTOR" title="JSTOR">JSTOR</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://jstor.org/stable/86249">86249</a></span>, <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1932PNAS...18..213E">1932PNAS...18..213E</a></span>, <a href="/wiki/Semantic_Scholar" title="Semantic Scholar">S2CID</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:19351448">19351448</a></span>, <a rel="nofollow" class="external text" href="https://www.pnas.org/doi/epdf/10.1073/pnas.18.3.213">lire en ligne</a> <span typeof="mw:File"><span title="Accès libre au document"><img alt="Accès libre" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span> <abbr class="abbr indicateur-format format-pdf" title="Document au format Portable Document Format (PDF) d'Adobe">[PDF]</abbr>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+the+relation+between+the+expansion+and+the+mean+density+of+the+Universe&rft.jtitle=PNAS&rft.issue=3&rft.aulast=Einstein&rft.aufirst=Albert&rft.au=de+Sitter%2C+Willem&rft.date=1932-03-15&rft.volume=18&rft_id=info%3Adoi%2F10.1073%2Fpnas.18.3.213&rft_id=info%3Apmid%2F16587663&rft_id=info%3Aoclcnum%2F9985762814&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>.</li> <li><span class="ouvrage" id="KraghOverduin2014"><span class="ouvrage" id="Helge_S._KraghJames_M._Overduin2014"><small>[Kragh et Overduin 2014]</small> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> <a href="/wiki/Helge_Kragh" title="Helge Kragh">Helge S. <span class="nom_auteur">Kragh</span></a> et James M. <span class="nom_auteur">Overduin</span>, <cite class="italique" lang="en">The weight of the vacuum : a scientific history of dark energy</cite>, Berlin et Heidelberg, <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>, <abbr class="abbr" title="collection">coll.</abbr> « Springerbriefs in physics », <time class="nowrap" datetime="2014-06" data-sort-value="2014-06">juin 2014</time>, <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="8"><span class="romain" style="text-transform:uppercase">VIII</span></abbr>-113 <abbr class="abbr" title="pages">p.</abbr>, 15,5 × 23,5 <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-3-642-55089-8" title="Spécial:Ouvrages de référence/978-3-642-55089-8"><span class="nowrap">978-3-642-55089-8</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9783642550898" title="Spécial:Ouvrages de référence/9783642550898"><span class="nowrap">9783642550898</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/884863929">884863929</a></span>, <a href="/wiki/Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007/978-3-642-55090-4">10.1007/978-3-642-55090-4</a></span>, <a href="/wiki/Semantic_Scholar" title="Semantic Scholar">S2CID</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:123876355">123876355</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/179851837">179851837</a></span>, <a rel="nofollow" class="external text" href="https://link.springer.com/book/10.1007/978-3-642-55090-4">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=sroqBAAAQBAJ">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+weight+of+the+vacuum&rft.place=Berlin+et+Heidelberg&rft.pub=Springer&rft.edition=1&rft.stitle=a+scientific+history+of+dark+energy&rft.aulast=Kragh&rft.aufirst=Helge+S.&rft.au=Overduin%2C+James+M.&rft.date=2014-06&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%228%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EVIII%3C%2Fspan%3E%3C%2Fabbr%3E-113&rft.isbn=978-3-642-55089-8&rft_id=info%3Adoi%2F10.1007%2F978-3-642-55090-4&rft_id=info%3Aoclcnum%2F884863929&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>.</li> <li><span class="ouvrage" id="Hooper2024"><span class="ouvrage" id="Dan_Hooper2024"><small>[Hooper 2024]</small> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Dan <span class="nom_auteur">Hooper</span> (avant-propos d'<a href="/wiki/Edward_Kolb" title="Edward Kolb">Edward W. Kolb</a> et <a href="/wiki/Michael_Turner_(cosmologue)" title="Michael Turner (cosmologue)">Michael S. Turner</a>), <cite class="italique" lang="en">Particle cosmology and astrophysics</cite>, Princeton et Oxford, <a href="/wiki/Princeton_University_Press" title="Princeton University Press">PUP</a>, hors <abbr class="abbr" title="collection">coll.</abbr>, <time class="nowrap" datetime="2024-05" data-sort-value="2024-05">mai 2024</time>, <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="26"><span class="romain" style="text-transform:uppercase">XXVI</span></abbr>-422 <abbr class="abbr" title="pages">p.</abbr>, 21,6 × 26,7 <abbr class="abbr" title="centimètre">cm</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-0-691-23504-2" title="Spécial:Ouvrages de référence/978-0-691-23504-2"><span class="nowrap">978-0-691-23504-2</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9780691235042" title="Spécial:Ouvrages de référence/9780691235042"><span class="nowrap">9780691235042</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/1387008549">1387008549</a></span>, <a rel="nofollow" class="external text" href="https://press.princeton.edu/books/hardcover/9780691235042/particle-cosmology-and-astrophysics">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=JK_jEAAAQBAJ">lire en ligne</a>)</small>, <abbr class="abbr" title="première">I<sup>re</sup></abbr> partie (« Preliminaries »), <abbr class="abbr" title="chapitre(s)">chap.</abbr> 2<span class="lang-en" lang="en"> (« General relativity and Friedmann equations »)</span>, <abbr class="abbr" title="pages">p.</abbr> <span class="nowrap">11-29</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Particle+cosmology+and+astrophysics&rft.atitle=General+relativity+and+Friedmann+equations&rft.place=Princeton+et+Oxford&rft.pub=PUP&rft.edition=1&rft.aulast=Hooper&rft.aufirst=Dan&rft.date=2024-05&rft.pages=11-29&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%2226%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EXXVI%3C%2Fspan%3E%3C%2Fabbr%3E-422&rft.isbn=978-0-691-23504-2&rft_id=info%3Aoclcnum%2F1387008549&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>.</li> <li><span class="ouvrage" id="LiddleLyth2000"><span class="ouvrage" id="Andrew_R._LiddleDavid_H._Lyth2000"><small>[Liddle et Lyth 2000]</small> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> <a href="/wiki/Andrew_Liddle" title="Andrew Liddle">Andrew R. <span class="nom_auteur">Liddle</span></a> et <a href="/wiki/David_Lyth" title="David Lyth">David H. <span class="nom_auteur">Lyth</span></a>, <cite class="italique" lang="en">Cosmological inflation and large-scale structure</cite>, Cambridge, <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">CUP</a>, hors <abbr class="abbr" title="collection">coll.</abbr>, <time class="nowrap" datetime="2000-04" data-sort-value="2000-04">avril 2000</time> (<abbr class="abbr" title="réimpression">réimpr.</abbr> <time class="nowrap" datetime="2000-06" data-sort-value="2000-06">juin 2000</time>), <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="13"><span class="romain" style="text-transform:uppercase">XIII</span></abbr>-400 <abbr class="abbr" title="pages">p.</abbr>, 17,8 × 25,4 <abbr class="abbr" title="centimètre">cm</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-0-521-66022-8" title="Spécial:Ouvrages de référence/978-0-521-66022-8"><span class="nowrap">978-0-521-66022-8</span></a> et <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-0-521-57598-0" title="Spécial:Ouvrages de référence/978-0-521-57598-0"><span class="nowrap">978-0-521-57598-0</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9780521660228" title="Spécial:Ouvrages de référence/9780521660228"><span class="nowrap">9780521660228</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/490395238">490395238</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb37563056s.public">37563056</a></span>, <a href="/wiki/Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1017/CBO9781139175180">10.1017/CBO9781139175180</a></span>, <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000cils.book.....L">2000cils.book.....L</a></span>, <a href="/wiki/Semantic_Scholar" title="Semantic Scholar">S2CID</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:260519017">260519017</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/052231933">052231933</a></span>, <a rel="nofollow" class="external text" href="https://www.cambridge.org/fr/universitypress/subjects/physics/astrophysics/cosmological-inflation-and-large-scale-structure">présentation en ligne</a>, <a rel="nofollow" class="external text" href="https://fma.if.usp.br/~mlima/teaching/PGF5292_2021/LiddleLyth_CILSS.pdf">lire en ligne</a> <span typeof="mw:File"><span title="Accès libre au document"><img alt="Accès libre" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span> <abbr class="abbr indicateur-format format-pdf" title="Document au format Portable Document Format (PDF) d'Adobe">[PDF]</abbr>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cosmological+inflation+and+large-scale+structure&rft.place=Cambridge&rft.pub=CUP&rft.edition=1&rft.aulast=Liddle&rft.aufirst=Andrew+R.&rft.au=Lyth%2C+David+H.&rft.date=2000-04&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%2213%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EXIII%3C%2Fspan%3E%3C%2Fabbr%3E-400&rft_id=info%3Adoi%2F10.1017%2FCBO9781139175180&rft_id=info%3Aoclcnum%2F490395238&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>.</li> <li><span class="ouvrage" id="Taillet2023"><span class="ouvrage" id="Richard_Taillet2023"><small>[Taillet 2023]</small> Richard <span class="nom_auteur">Taillet</span>, <cite style="font-style:normal">« Univers de Friedmann-Lemaître et expansion cosmologique »</cite>, dans Natalie Webb (dir.), <cite class="italique">Gravitation</cite>, Londres, <a href="/wiki/ISTE_Group" title="ISTE Group">ISTE</a>, <abbr class="abbr" title="collection">coll.</abbr> « Encyclopédie : sciences / Univers : cosmologie et relativité générale », <time class="nowrap" datetime="2023-03" data-sort-value="2023-03">mars 2023</time>, <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="8"><span class="romain" style="text-transform:uppercase">VIII</span></abbr>-352 <abbr class="abbr" title="pages">p.</abbr>, 15,2 × 22,9 <abbr class="abbr" title="centimètre">cm</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-1-78948-120-4" title="Spécial:Ouvrages de référence/978-1-78948-120-4"><span class="nowrap">978-1-78948-120-4</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9781789481204" title="Spécial:Ouvrages de référence/9781789481204"><span class="nowrap">9781789481204</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/1377288035">1377288035</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb47234398r.public">47234398</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/269367470">269367470</a></span>, <a rel="nofollow" class="external text" href="https://www.istegroup.com/fr/produit/gravitation/">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=TUq1EAAAQBAJ">lire en ligne</a>)</small>, <span class="nowrap"><abbr class="abbr" title="chapitre(s)">chap.</abbr> 4</span>, <abbr class="abbr" title="pages">p.</abbr> <span class="nowrap">261-344</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.btitle=Gravitation&rft.atitle=Univers+de+Friedmann-Lema%C3%AEtre+et+expansion+cosmologique&rft.place=Londres&rft.pub=ISTE&rft.edition=1&rft.aulast=Taillet&rft.aufirst=Richard&rft.date=2023-03&rft.pages=261-344&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%228%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EVIII%3C%2Fspan%3E%3C%2Fabbr%3E-352&rft.isbn=978-1-78948-120-4&rft_id=info%3Aoclcnum%2F1377288035&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>.</li> <li><span class="ouvrage" id="Wands2014"><span class="ouvrage" id="David_Wands2014"><small>[Wands 2014]</small> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> <a href="/wiki/David_Wands" title="David Wands">David <span class="nom_auteur">Wands</span></a>, <cite style="font-style:normal" lang="en">« Friedmann-Lemaître-Robertson-Walker cosmology »</cite>, dans <a href="/wiki/Abhay_Ashtekar" title="Abhay Ashtekar">Abhay Ashtekar</a> et Vesselin Petkov (éd. et <abbr class="abbr" title="préface">préf.</abbr>), <cite class="italique" lang="en">Springer handbook of spacetime</cite>, Berlin et Heidelberg, <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>, <abbr class="abbr" title="collection">coll.</abbr> « Springer handbooks », <time class="nowrap" datetime="2014-07" data-sort-value="2014-07">juillet 2014</time>, <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="26"><span class="romain" style="text-transform:uppercase">XXVI</span></abbr>-887 <abbr class="abbr" title="pages">p.</abbr>, 18,5 × 24,6 <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-3-642-41991-1" title="Spécial:Ouvrages de référence/978-3-642-41991-1"><span class="nowrap">978-3-642-41991-1</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9783642419911" title="Spécial:Ouvrages de référence/9783642419911"><span class="nowrap">9783642419911</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/894030364">894030364</a></span>, <a href="/wiki/Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007/978-3-642-41992-8">10.1007/978-3-642-41992-8</a></span>, <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014shst.book.....A">2014shst.book.....A</a></span>, <a href="/wiki/Semantic_Scholar" title="Semantic Scholar">S2CID</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118297210">118297210</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/181485206">181485206</a></span>, <a rel="nofollow" class="external text" href="https://link.springer.com/book/10.1007/978-3-642-41992-8">présentation en ligne</a>, <a rel="nofollow" class="external text" href="http://strangebeautiful.com/other-texts/ashtekar-petkov-springer-hndbk-st.pdf">lire en ligne</a> <span typeof="mw:File"><span title="Accès libre au document"><img alt="Accès libre" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span> <abbr class="abbr indicateur-format format-pdf" title="Document au format Portable Document Format (PDF) d'Adobe">[PDF]</abbr>)</small>, <span class="nowrap">partie E</span> (« General relativity and the universe »), <span class="nowrap"><abbr class="abbr" title="chapitre(s)">chap.</abbr> 30</span>, <abbr class="abbr" title="pages">p.</abbr> <span class="nowrap">657-671</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.btitle=Springer+handbook+of+spacetime&rft.atitle=Friedmann-Lema%C3%AEtre-Robertson-Walker+cosmology&rft.place=Berlin+et+Heidelberg&rft.pub=Springer&rft.edition=1&rft.aulast=Wands&rft.aufirst=David&rft.date=2014-07&rft.pages=657-671&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%2226%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EXXVI%3C%2Fspan%3E%3C%2Fabbr%3E-887&rft.isbn=978-3-642-41991-1&rft_id=info%3Adoi%2F10.1007%2F978-3-642-41992-8&rft_id=info%3Aoclcnum%2F894030364&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADensit%C3%A9+critique"></span></span></span>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Article_connexe">Article connexe</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=10" title="Modifier la section : Article connexe" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=10" title="Modifier le code source de la section : Article connexe"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Table_des_constantes_astrophysiques" class="mw-redirect" title="Table des constantes astrophysiques">Table des constantes astrophysiques</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Liens_externes">Liens externes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Densit%C3%A9_critique&veaction=edit&section=11" title="Modifier la section : Liens externes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Densit%C3%A9_critique&action=edit&section=11" title="Modifier le code source de la section : Liens externes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="ouvrage" id="Ridpath2012"><span class="ouvrage" id="Ian_Ridpath2012"><small>[Ridpath 2012]</small> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> <a href="https://en.wikipedia.org/wiki/en:Ian_Ridpath" class="extiw" title="w:en:Ian Ridpath">Ian <span class="nom_auteur">Ridpath</span></a>, « <a rel="nofollow" class="external text" href="https://www.oxfordreference.com/display/10.1093/oi/authority.20110803095648446"><cite style="font-style:normal;" lang="en">critical density</cite></a> » [« densité critique »], notice d'autorité <abbr class="abbr" title="numéro">n<sup>o</sup></abbr> 20110803095648446 <span typeof="mw:File"><span title="Accès libre au document"><img alt="Accès libre" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span>, <span class="italique">Oxford Reference</span>, Oxford, <a href="/wiki/Oxford_University_Press" title="Oxford University Press">OUP</a>, <time>2012</time></span></span>.</li> <li><span class="ouvrage">« <a rel="nofollow" class="external text" href="http://www.cnrs.fr/cw/dossiers/dosbig/decouv/xcroire/forPart/relativite/pop1_1.htm"><cite style="font-style:normal;">La densité critique de l'Univers</cite></a> » <span typeof="mw:File"><span title="Accès libre au document"><img alt="Accès libre" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span>, <span class="italique">Big Bang : des origines de l'Univers aux origines de la vie</span>, <i>SagaScience</i>, Paris, <a href="/wiki/Centre_national_de_la_recherche_scientifique" title="Centre national de la recherche scientifique">CNRS</a> <small style="line-height:1em;">(consulté le <time class="nowrap" datetime="2014-10-27" data-sort-value="2014-10-27">27 octobre 2014</time>)</small></span>.</li></ul> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint autocollapse" style=""> <tbody><tr><th class="navbox-title" colspan="2" style=""><div style="float:left; width:6em; text-align:left"><div class="noprint plainlinks nowrap tnavbar" style="padding:0; font-size:xx-small; color:var(--color-emphasized, #000000);"><a href="/wiki/Mod%C3%A8le:Palette_Mod%C3%A8les_cosmologiques" title="Modèle:Palette Modèles cosmologiques"><abbr class="abbr" title="Voir ce modèle.">v</abbr></a> · <a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Mod%C3%A8le:Palette_Mod%C3%A8les_cosmologiques&action=edit"><abbr class="abbr" title="Modifier ce modèle. Merci de prévisualiser avant de sauvegarder.">m</abbr></a></div></div><div style="font-size:110%"><a href="/wiki/Mod%C3%A8le_cosmologique" title="Modèle cosmologique">Modèles cosmologiques</a></div></th> </tr> <tr> <th class="navbox-group" style=""><a href="/wiki/Th%C3%A9orie" title="Théorie">Théories</a></th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Atome_primitif" title="Atome primitif">Atome primitif</a></li> <li><a href="/wiki/Classification_de_Bianchi" title="Classification de Bianchi">Classification de Bianchi</a></li> <li><a href="/wiki/Cosmologie_branaire" title="Cosmologie branaire">Cosmologie branaire</a></li> <li><a href="/wiki/Cosmologie_cordiste" title="Cosmologie cordiste">Cosmologie cordiste</a></li> <li><a href="/wiki/Dimensions_suppl%C3%A9mentaires" title="Dimensions supplémentaires">Dimensions supplémentaires</a></li> <li><a href="/wiki/Espace_anti_de_Sitter" title="Espace anti de Sitter">Espace anti de Sitter</a></li> <li><a href="/wiki/Espace_de_de_Sitter" title="Espace de de Sitter">Espace de Sitter</a></li> <li><a href="/wiki/Espace_de_Taub-NUT" title="Espace de Taub-NUT">Espace de Taub-NUT</a></li> <li><a href="/wiki/Expansion_de_l%27Univers" title="Expansion de l'Univers">Expansion de l'Univers</a> <ul><li><a href="/wiki/Acc%C3%A9l%C3%A9ration_de_l%27expansion_de_l%27Univers" title="Accélération de l'expansion de l'Univers">Accélération de l'expansion de l'Univers</a></li></ul></li> <li><a href="/wiki/Gravit%C3%A9_quantique" title="Gravité quantique">Gravité quantique</a></li> <li><a href="/wiki/Inflation_cosmique" title="Inflation cosmique">Inflation cosmique</a></li> <li><a href="/wiki/Th%C3%A9orie_des_cordes" title="Théorie des cordes">Théorie des cordes</a></li> <li><a href="/wiki/Univers_de_Milne" title="Univers de Milne">Univers de Milne</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style=""><a href="/wiki/Principe_physique" title="Principe physique">Principes</a></th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Principe_anthropique" title="Principe anthropique">Principe anthropique</a></li> <li><a href="/wiki/Principes_cosmologiques" title="Principes cosmologiques">Principes cosmologiques</a></li> <li><a href="/wiki/Principe_cosmologique_parfait" title="Principe cosmologique parfait">Principe cosmologique parfait</a></li> <li><a href="/wiki/Principe_de_Copernic" title="Principe de Copernic">Principe de Copernic</a></li> <li><a href="/wiki/Principe_de_m%C3%A9diocrit%C3%A9" title="Principe de médiocrité">Principe de médiocrité</a></li> <li><a href="/wiki/Causalit%C3%A9_(physique)" title="Causalité (physique)">Principe de causalité</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style=""><a href="/wiki/Histoire_et_chronologie_de_l%27Univers" title="Histoire et chronologie de l'Univers">Histoire</a> et<br /><a href="/wiki/Destin_de_l%27Univers" title="Destin de l'Univers">destin de l'Univers</a></th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Pr%C3%A9-Big_Bang" title="Pré-Big Bang">Pré-Big Bang</a></li> <li><a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a></li> <li><a href="/wiki/Univers_primordial" title="Univers primordial">Univers primordial</a></li> <li><a href="/wiki/Frise_chronologique_du_Big_Bang" title="Frise chronologique du Big Bang">Frise chronologique du Big Bang</a></li> <li><a href="/wiki/%C3%88re_de_Planck" title="Ère de Planck">Ère de Planck</a></li> <li><a href="/wiki/Big_Bounce" title="Big Bounce">Big Bounce <i>alias</i> Univers phénix</a></li> <li><a href="/wiki/Mort_thermique_de_l%27Univers" title="Mort thermique de l'Univers">Big Chill <i>alias</i> Mort thermique de l'Univers</a></li> <li><a href="/wiki/Big_Crunch" title="Big Crunch">Big Crunch</a></li> <li><a href="/wiki/Grand_d%C3%A9chirement" title="Grand déchirement">Grand déchirement</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style=""><a href="/wiki/Mod%C3%A8le_standard_de_la_cosmologie" title="Modèle standard de la cosmologie">Modèle standard</a></th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Mod%C3%A8le_%CE%9BCDM" title="Modèle ΛCDM">Modèle ΛCDM</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style=""><a href="/wiki/Cosmologie_non_standard" title="Cosmologie non standard">Modèles non-standard</a></th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Mod%C3%A8le_cyclique" title="Modèle cyclique">Modèle cyclique</a> <ul><li><a href="/wiki/Cosmologie_cyclique_conforme" title="Cosmologie cyclique conforme">Cosmologie cyclique conforme</a></li></ul></li> <li><a href="/wiki/Mod%C3%A8le_OCDM" title="Modèle OCDM">Modèle OCDM</a></li> <li><a href="/wiki/Mod%C3%A8le_SCDM" title="Modèle SCDM">Modèle SCDM</a></li> <li><a href="/wiki/Mod%C3%A8le_cosmologique_bi-m%C3%A9trique" title="Modèle cosmologique bi-métrique">Modèles cosmologiques bi-métriques</a></li> <li><a href="/wiki/Th%C3%A9orie_de_l%27%C3%A9tat_stationnaire" title="Théorie de l'état stationnaire">Théorie de l'état stationnaire</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style=""><a href="/wiki/Param%C3%A8tre_cosmologique" title="Paramètre cosmologique">Paramètres</a></th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/%C3%82ge_de_l%27Univers" title="Âge de l'Univers">Âge de l'Univers</a></li> <li><a href="/wiki/Constante_cosmologique" title="Constante cosmologique">Constante cosmologique</a></li> <li><a href="/wiki/Constante_de_Hubble" title="Constante de Hubble">Constante de Hubble</a></li> <li><a href="/wiki/%C3%89nergie_sombre" title="Énergie sombre">Énergie noire</a></li> <li><a href="/wiki/Indice_spectral" title="Indice spectral">Indice spectral</a></li> <li><a href="/wiki/Mati%C3%A8re_baryonique" title="Matière baryonique">Matière baryonique</a></li> <li><a href="/wiki/Mati%C3%A8re_noire" title="Matière noire">Matière noire</a></li> <li><a href="/wiki/Param%C3%A8tre_de_densit%C3%A9" title="Paramètre de densité">Paramètre de densité</a></li> <li><a href="/wiki/R%C3%A9ionisation" title="Réionisation">Réionisation</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Types</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Univers_d%27Einstein" title="Univers d'Einstein">Univers d'Einstein</a></li> <li><a href="/wiki/M%C3%A9trique_de_Friedmann-Lema%C3%AEtre-Robertson-Walker" title="Métrique de Friedmann-Lemaître-Robertson-Walker">Univers de Friedmann-Lemaître-Robertson-Walker</a></li> <li><a href="/wiki/Univers_de_G%C3%B6del" title="Univers de Gödel">Univers de Gödel</a></li> <li><a href="/wiki/Univers_de_Milne" title="Univers de Milne">Univers de Milne</a></li> <li><a href="/wiki/Univers_de_de_Sitter" title="Univers de de Sitter">Univers de de Sitter</a></li> <li><a href="/wiki/Univers_ekpyrotique" title="Univers ekpyrotique">Univers ekpyrotique</a></li> <li><a href="/wiki/Univers_en_tore_bidimensionnel" title="Univers en tore bidimensionnel">Univers en tore bidimensionnel</a></li> <li><a href="/wiki/Univers_fractal" title="Univers fractal">Univers fractal</a></li> <li><a href="/wiki/Univers_h%C3%A9sitant" title="Univers hésitant">Univers hésitant</a></li> <li><a href="/wiki/Univers_mixmaster" title="Univers mixmaster">Univers mixmaster</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Problèmes</th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Probl%C3%A8me_de_l%27horizon" title="Problème de l'horizon">Problème de l'horizon</a></li> <li><a href="/wiki/Probl%C3%A8me_de_la_formation_des_structures" title="Problème de la formation des structures">Problème de la formation des structures</a></li> <li><a href="/wiki/Probl%C3%A8me_de_la_platitude" title="Problème de la platitude">Problème de la platitude</a></li> <li><a href="/wiki/Asym%C3%A9trie_baryonique" title="Asymétrie baryonique">Asymétrie baryonique</a></li> <li><a href="/wiki/Probl%C3%A8me_des_baryons_manquants" title="Problème des baryons manquants">Problème des baryons manquants</a></li> <li><a href="/wiki/Courbe_de_rotation_des_galaxies" title="Courbe de rotation des galaxies">Problème de la rotation des galaxies</a></li> <li><a href="/wiki/Acc%C3%A9l%C3%A9ration_de_l%27expansion_de_l%27Univers" title="Accélération de l'expansion de l'Univers">Problème de l'accélération de l'expansion de l'Univers</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Autres concepts</th> <td class="navbox-list" style=""><table class="navbox-subgroup" style=""> <tbody><tr> <td class="navbox-list" style=";" colspan="2"><div class="liste-horizontale"> <ul><li><a href="/wiki/Courbure_spatiale" title="Courbure spatiale">Courbure spatiale</a></li> <li><a class="mw-selflink selflink">Densité critique</a></li> <li><a href="/wiki/Forme_de_l%27Univers" title="Forme de l'Univers">Forme de l'Univers</a></li> <li><a href="/wiki/Horizon_cosmologique" title="Horizon cosmologique">Horizon cosmologique</a></li> <li><a href="/wiki/Horizon_des_%C3%A9v%C3%A9nements" title="Horizon des événements">Horizon des événements</a></li> <li><a href="/wiki/Horizon_des_particules" title="Horizon des particules">Horizon des particules</a></li> <li><a href="/wiki/Masse_de_l%27Univers" title="Masse de l'Univers">Masse de l'Univers</a></li> <li><a href="/wiki/Univers_observable" title="Univers observable">Univers observable</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Non scientifique</th> <td class="navbox-list navbox-even" style=";"><div class="liste-horizontale"> <ul><li><a href="/wiki/Cosmologie_religieuse" title="Cosmologie religieuse">Cosmologie religieuse</a></li> <li><a href="/wiki/Cosmogonie" title="Cosmogonie">Cosmogonie</a></li> <li><a href="/wiki/Cr%C3%A9ationnisme" title="Créationnisme">Créationnisme</a></li> <li><a href="/wiki/Dessein_intelligent" title="Dessein intelligent">Dessein intelligent</a></li></ul> </div></td> </tr> </tbody></table></td> </tr> <tr> <td class="navbox-banner" style="" colspan="2"><div class="liste-horizontale"> <ul><li><a href="/wiki/Univers" title="Univers">Univers</a></li> <li><a href="/wiki/Cosmologie" title="Cosmologie">Cosmologie</a></li> <li><a href="/wiki/Multivers" title="Multivers">Multivers</a></li></ul> </div></td></tr></tbody></table> </div> <ul id="bandeau-portail" class="bandeau-portail"><li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer skin-invert-image" typeof="mw:File"><a href="/wiki/Portail:Cosmologie" title="Portail de la cosmologie"><img alt="icône décorative" 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