Higher order moments of the density field in a parametrized sequence of non-Gaussian theories

Abstract

We calculate the higher order moments in a sequence of models where the initial density fluctuations are drawn from a distribution with a power-law power spectrum. For large values of ν, the distribution is approximately Gaussian, and we reproduce the values known from perturbation theory. As ν is lowered the distribution becomes progressively more non-Gaussian, approximating models with rare, high-amplitude peaks. The limit ν=1 is a realization of recently proposed isocurvature models for producing early galaxy formation, where the density perturbations are quadratic in a Gaussian field.