Cosmological Perturbation Theory and the Spherical Collapse model : Part II . Non - Gaussian initial conditions

In Part I of this series, we introduced the Spherical Collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants ξJ 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 contributions up to terms involving non-local integrals of the J-point functions. We argue that for the hierarchical ratios SJ , 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 this analytic results to Non-Gaussian N-body simulations, which turn out to be in very good agreement up to scales where σ ∼ < 1.