Cosmological perturbation theory and the spherical collapse model — II. Non-Gaussian initial conditions |
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| Authors: | Enrique Gaztañaga & Pablo Fosalba |
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| Institution: | Institut d'Estudis Espacials de Catalunya, Research Unit (CSIC), Edf. Nexus-201 - c/ Gran Capità2-4, 08034 Barcelona, Spain |
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| Abstract: | In Paper I of this series, we introduced the spherical collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants ξ 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 subdominant 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 with non-Gaussian N -body simulations, which turn out to be in very good agreement up to scales where σ ≲ 1. |
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| Keywords: | methods: analytical methods: numerical galaxies: clusters: general cosmology: theory large-scale structure of Universe |
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