Dynamics of gravitational clustering

Free access article

Issue		A&A Volume 382, Number 2, February I 2002


Page(s)		431 - 449
Section		Cosmology
DOI		http://dx.doi.org/10.1051/0004-6361:20011675

A&A 382, 431-449 (2002)
DOI: 10.1051/0004-6361:20011675

III. The quasi-linear regime for some non-Gaussian initial conditions

P. Valageas

Service de Physique Théorique, CEN Saclay, 91191 Gif-sur-Yvette, France

(Received 11 July 2001 / Accepted 23 November 2001 )

Abstract
Using a non-perturbative method developed in a previous work (Paper II), we derive the probability distribution ${\cal P}(\delta_{R})$ of the density contrast within spherical cells in the quasi-linear regime for some non-Gaussian initial conditions. We describe three such models. The first one is a straightforward generalization of the Gaussian scenario. It can be seen as a phenomenological description of a density field where the tails of the linear density contrast distribution would be of the form ${\cal P}_{\rm L}(\delta_{\rm L}) \sim {\rm e}^{-\vert\delta_{\rm L}\vert^{-\alpha}}$ , where $\alpha$ is no longer restricted to 2 (as in the Gaussian case). We derive exact results for ${\cal P}(\delta_{R})$ in the quasi-linear limit. The second model is a physically motivated isocurvature CDM scenario. Our approach needs to be adapted to this specific case and in order to get convenient analytical results we introduce a simple approximation (which is not related to the gravitational dynamics but to the initial conditions). Then, we find a good agreement with the available results from numerical simulations for the pdf of the linear density contrast for $\delta_{{\rm L},R} \ga 0$ . We can expect a similar accuracy for the non-linear pdf ${\cal P}(\delta_{R})$ . Finally, the third model corresponds to the small deviations from Gaussianity which arise in standard slow-roll inflation. We obtain exact results for the pdf of the density field in the quasi-linear limit, to first-order over the primordial deviations from Gaussianity.

Key words: cosmology: theory -- large-scale structure of Universe

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