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COSMOLOGIE
Partie 4: Courbure de l'univers
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Deuxième équation de Friedman
nSoit H, la const= ante de Hubble, r sont rayon et soit e la pression de radiation de l'univers:
<= span class=3DBB style=3D'position:absolute;left:-4.43%;top:.39em'>nH2<= /span>+k/r2<= /span> proportionnel à e
<= span class=3DBB style=3D'position:absolute;left:-4.35%;top:.39em'>nOn ve= ut connaître r, le rayon de l'univers.
nOn pe= ut mesurer H et e mais il faudrait = = connaître k. nQu'est-ce donc que ce fameux paramètre manquant.
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Trois valeurs possibles
<= span class=3DBB style=3D'position:absolute;left:-4.43%;top:.39em'>n Le paramètre k peut avoir 3 valeurs
n-Si c'est 0, l'univers est plat
n-Si c'est +1 l'univers est sphérique
n-Si k=3D-1, l'univers est hyperbolique
------=_NextPart_01C92714.3F531B10 Content-Location: file:///C:/5D14ACD4/COSMOLOGIE4_files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" COSMOLOGIE
L'univers comme un gaz
nCe dont ce sont = rendu compte Gamov, Lemaître et Friedman, c'est que le comportemen= t = mathématique de l'univers en expansion était comme un gaz en expansion<= /span>
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Dans un gaz réel
nGaz dans un ballon
= pression
température
Quantité de gaz
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Ou comme dans un piston
nSuppo= sons le contenu de l'univers comme le gaz dans un piston
Univers au début:
Gaz compressé
Et chaud
Plus l'univers s'agrandit,
Plus sa température baisse
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Et ensuite?
<= span class=3DBB style=3D'position:absolute;left:-4.43%;top:.39em'>nL'uni= vers va en s'agrandissant
<= span class=3DBB style=3D'position:absolute;left:-4.43%;top:.39em'>nIl se refroidit en s'agrandissant
<= span class=3DBB style=3D'position:absolute;left:-4.43%;top:.39em'>nComme= nt s'aggrandit-il?
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La constante de Hubble
nCe que Hubble a découvert est que pl= us les galaxies sont loin, plus elles vont vite.
<= span class=3DBB style=3D'position:absolute;left:-4.43%;top:.39em'>nSa co= nstante est de 76 km/s/Mpsec
n
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Rempla&= ccedil;ons le ballon par l'univers
<= span class=3DBB style=3D'position:absolute;left:-4.43%;top:.39em'>nVites= se d'expansion proportionnelle à :
<= span class=3DBB style=3D'position:absolute;left:-4.43%;top:.39em'>n-4pG(= r+3p)
n où r est la densité de matière/énergie de l'univers et n où p est la pression exercée par la radiation (lumière)
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Quelques unités
nUn parsec c'est la distance à laquelle on verrait l'orbite de la terre sous un angle de 1" d'arc
<= span class=3DBB style=3D'position:absolute;left:-4.43%;top:.39em'>nCela = vaut 3,2 années lumières
<= span class=3DBB style=3D'position:absolute;left:-4.21%;top:.39em'>n1 Mps= ec vaut 3,2 millions d'années lumière
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= Vous êtes ici
= ;
Avec vos télescopes vous regardez par là
Vous regardez vers le passé
= ;
LA CONSTANTE DE HUBBLE MONTRE QUE L'UNIVERS
ALLAIT PLUS VITE DANS LE PASSÉ
3D"POUR
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IL RESTE UNE QUESTION
oL'expansion ira-t-elle tou= jours en ralentissant?
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La courbure de l'univers
oLa réponse exige de connaître la courbure de l'univers
<= span class=3DBB style=3D'position:absolute;left:-5.85%'>oVoyons d'abord = les forces en action
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Les forces en action
nAu début l'univers n'était composé que de lumière. La pression qui a repoussé l'univers si vite est la pression de la lumière, la pression de radiation
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Difficile à croire mais vrai
oIl est difficile de croire= que la lumière puisse exercer une pression.  Lorsque vous sortez dehor= s au soleil, vous ne vous sentez pas projetés par derriè= ;re!
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C'est pourtant la lumière
oC'est pourtant la pression= de radiation qui maintient les étoiles comme le soleil en équilibre
Gravit= é
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