Cosmological Perturbation Theory and the Spherical Collapse Model - II. Non-Gaussian initial conditions

Details Cosmological Perturbation Theory and the Spherical Collapse Model - II. Non-Gaussian initial conditions Cosmological Perturbation Theory and the Spherical Collapse Model - II. Non-Gaussian initial conditions

1997-12-18

arxiv.org/abs/astro-ph/9712263v2

Mon.Not.Roy.Astron.Soc. 301 (1998) 524

Astronomy and Astrophysics

Astrophysics

12 pages, Latex, 8 figures. New section with predictions for the Isocurvature CDM cosmogony added. Accepted for publication in

Scientific paper

10.1046/j.1365-8711.1998.02034.x

In Part I of this series, we introduced the Spherical Collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants $\xi_J$ of density fluctuations in cosmological Perturbation Theory (PT). Within this approximation, the dynamics is decoupled from the statistics of the initial conditions, so we are able to present here the cumulants for generic Non-Gaussian initial conditions, which can be estimated to arbitrary order including the smoothing effects. The SC model turns out to recover the exact leading-order non-linear contributions up to terms involving non-local integrals of the $J$-point functions. We argue that for the hierarchical ratios $S_J$, these non-local terms are sub-dominant and tend to compensate each other. The resulting predictions show a non-trivial time evolution that can be used to discriminate between models of structure formation. We compare these analytic results to Non-Gaussian N-body simulations, which turn out to be in very good agreement up to scales where $\sigma \simlt 1$.

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