Dynamics of gravitational clustering III. The quasi-linear regime for some non-Gaussian initial conditions

Abstract

Using a non-perturbative method developed in a previous work (paper II), we derive the probability distribution $P(\delta_R)$ 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 $P_L(\delta_L) \sim e^{-|\delta_L|^{-\alpha}}$, where $\alpha$ is no longer restricted to 2 (as in the Gaussian case). We derive exact results for $P(\delta_R)$ 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 $\delta_{L,R} \ga 0$. We can expect a similar accuracy for the non-linear pdf $P(\delta_R)$. 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.