Cosmological perturbation theory and the spherical collapse model - II. Non-Gaussian initial conditions

In Paper I of this series, we introduced the spherical collapse (SC) approx imation 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-G aussian initial conditions, which can be estimated to arbitrary order inclu ding the smoothing effects. The SC model turns out to recover the exact lea ding-order non-linear contributions up to terms involving non-local integra ls 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, T he resulting predictions show a non-trivial time evolution that can be used to discriminate between models of structure formation. We compare these an alytic results with non-Gaussian N-body simulations, which turn out to be i n very good agreement up to scales where sigma less than or similar to l.