We show that the cosmological constant favours significantly the growth of
voids in the universe. This dynamical effect is investigated within a newtonian
approach with an extension to Friedmann-Lema\^{\i}tre model.Comment: to appea

Fliche, Henri-Hugues

Triay, Roland

English

arXiv

to appearWe show that the cosmological constant favours significantly the growth of voids in the universe. This dynamical effect is investigated within a newtonian approach with an extension to Friedmann-Lema\^{\i}tre model

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SPHERICAL VOIDS IN NEWTON-FRIEDMANNUNIVERSERoland Triay, Henri-Hugues FlicheTo cite this version:Roland Triay, Henri-Hugues Fliche. SPHERICAL VOIDS IN NEWTON-FRIEDMANN UNI-VERSE. H. Kleinert, R.T. Jantzen and R. Ruffini. Proceedings of the Eleventh Marcel Gross-mann Meeting on General Relativity, 2007, Berlin, Germany. World Scientific, Singapore, 2007.<hal-00089276>HAL Id: hal-00089276https://hal.archives-ouvertes.fr/hal-00089276Submitted on 16 Aug 2006HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.ccsd-00089276, version 1 - 16 Aug 2006August 16, 2006 17:35 WSPC - Proceedings Trim Size: 9.75in x 6.5in main.hyper123301SPHERICAL VOIDS IN NEWTON-FRIEDMANN UNIVERSER. TRIAYCentre de Physique The´orique ∗CNRS Luminy Case 907, 13288 Marseille Cedex 9, France∗E-mail: triay@cpt.univ-mrs.frwww.cpt.univ-mrs.frH. H. FLICHELMMT†, Fac. des Sciences et Techniques de St Je´roˆmeav. Normandie-Niemen, 13397 Marseille Cedex 20, FranceE-mail: henri-hugues.fliche@wanadoo.frThe understanding of voids formation, which is at the origin of the foam like pat-terns in the distribution of galaxies within scale up to 100 Mpc, has become an im-portant challenge for the large scale formation theory.23 Such a structure has beenobserved since three decades and confirmed by recent surveys.4,5,7,14–16,25,27 Investi-gations has been performed – on their statistical properties by improving identificationtechniques,24 by exploring their formation process in a Λ CDM model through N-bodysimulations,3,11,12,19,22,26,29 by probing their origins;21 – on the kinematics of giantvoids17 and the dynamics by testing models of void formation.1,2,10 Herein, we investi-gate the effect of the cosmological constant Λ on the evolution of a spherical void throughan exact solution of Euler-(modified) Poisson equations system (EPES).9 Let us remindthat Friedmann-Lemaˆıtre models, which provide us with a suitable description of theuniverse at large scales (thanks to their stability with respect to linear perturbations18),can be described within a Newtonian approach by means of EPES solutions for whomkinematics satisfy Hubble (cosmological) law. The void consists of three distinct media :a material shell (S) with null thickness and negligible tension-stress, an empty inside anda uniform dust distribution outside which expands according to Friedmann equation. Weuse a covariant formulation of EPES6,28 for deriving the evolution with time of S actingas boundaries condition for the inside and outside media.As a result, S expands with a huge initial burst that freezes asymptotically up tomatching Hubble flow. The related perturbation on redshift of sources located on S doesnot exceed ∆ z ∼ 10−3. In the Friedmann comoving frame, its magnification increasesnonlinearly with Ω◦ and Λ. These effects interpret respectively by the gravitationalattraction from the outer parts and repulsion (of vacuum) from the inner parts of S,with a sensitiveness on Ω at primordial epochs and on Λ later on by preserving theexpansion rate from an earlier decreasing. This dependence of the expansion velocity~v = yH~r on Λ is shown on Fig. 1 through the corrective factor y to Hubble expansion,where ~r and H stand respectively for radius of S and Hubble parameter at time t. Itis characterised by a protuberance at redshift z ∼ 1.7, the larger the Λ the higher the∗Unite´ Mixte de Recherche (UMR 6207) du CNRS, et des universite´s Aix-Marseille I, Aix-MarseilleII et du Sud Toulon-Var. Laboratoire affilie´ a` la FRUMAM (FR 2291).†UPRES EA 2596August 16, 2006 17:35 WSPC - Proceedings Trim Size: 9.75in x 6.5in main.hyper123302!!"!#$%!!"!&$'!!"!&11.11.21.3y-4 -2 0ln(a)"!"!&$(Fig. 1. The corrective factor y to Hubble expansion. It results from a void that initially expandswith Hubble flow at expansion parameter ai = 0.003, with Ω◦ = 0.3. and Ωλ = λ = 0, 0.7, 1.4.bump. It is due to the existence of a minimum value of Hubble parameter H whichis reached during the cosmological expansion (also referenced as a loitering period). 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Spherical Voids in Newton-Friedmann Universe

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