Discours sur l'origine de l'univers by Étienne Klein

By Étienne Klein

D'où vient l'univers ? Et d'où vient qu'il y a un univers ? Irrépressiblement, ces questions se posent à nous.

Et dès qu'un discours prétend nous éclairer, nous tendons l'oreille, avides d'entendre l'écho du tout optimal sign: les accélérateurs de particules vont bientôt nous révéler l'origine de l'univers en produisant des "big bang sous terre"; les données recueillies par le satellite tv for pc Planck nous dévoiler le "visage de Dieu"; certains disent même qu'en vertu de l. a. loi de los angeles gravitation l'univers a pu se créer de lui-même, à partir de rien...

Le grand dévoilement ne serait donc devenu qu'une affaire d'ultimes petits pas ? Rien n'est moins sûr... automobile de quoi parle l. a. body quand elle parle d'origine " ? Qu'est-ce que les théories actuelles sont réellement en mesure de nous révéler ?

A bien les examiner, les views que nous offre los angeles cosmologie contemporaine sont plus vertigineuses encore que tout ce que nous avons imaginé: l'univers a-t-il jamais commencé?

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42) b2 < 0 < b1 and x is the root of def χC (x) = + π + arccos x − b2 2 x + b2 2 1− b1 2 − x b1 2 + x − arccos 2 − b1 2 − x b1 2 + x 1− x − b2 2 x + b2 2 2 − x3/2 (t2 − t1 ). 43) 22 2 Exact solutions used in cosmology 5. Borderlines between cases Although the above cases cover all other eventualities in theory, the expressions for ψH , ψX , ΦH , etc. are not practical numerically near the borderlines between them, since very large terms are subtracted, creating excessive error. The series expansions that apply in the vicinity of the two borderlines – where the evolution is nearly parabolic, or nearly at maximum expansion at t2 – are given in Krasiński and Hellaby (2002) and Hellaby and Krasiński (2006).

3) the density distribution can be found for any instant. Initial velocity profile to a final density profile In this subsection we examine if there exists a solution of the evolution equations from a given initial velocity to a final density profile. e. t2 > t1 ⇒ R2 > R1 , with a positive value of the cosmological constant, Λ > 0. 2), therefore the values of E, Ri , M and Λ must be derived from the initial conditions. M (r) is again chosen to be the radial coordinate. 3) we can calculate R2 . 118) 38 2 Exact solutions used in cosmology where u = R1 ; we use u instead of R1 to emphasise that R1 is now an unknown variable.

1 The Lemaître–Tolman model 15 shells, and these constitute regular extrema in the spatial section of constant t. Both M,r and R,r change sign across a regular extremum. A closed model must necessarily have two origins and a spatial maximum (a ‘belly’). A vacuum model must necessarily have a spatial minimum (a ‘neck’ or ‘wormhole’). Necks may exist also in nonvacuum models, see Sec. 2 later in this text. Shell crossings, where a constant r shell collides with its neighbour, are loci of R,r = 0 that are not regular maxima or minima of R.

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