Gravitational Evolution of the Large-Scale Density Distribution: The Edgeworth & Gamma Expansions

Abstract

The gravitational evolution of the cosmic one-point Probability Distribution Function (PDF) can be estimated using an analytic approximation that combines gravitational Perturbation Theory (PT) with the Edgeworth expansion around a Gaussian PDF. We present an alternative to the Edgeworth series based on an expansion around the Gamma PDF, which is more appropriate to describe a realistic PDF. The Gamma expansion converges when the PDF exhibits exponential tails, which are predicted by PT and N-body simulations in the weakly non-linear regime (i.e, when the variance, ${\sigma }^2$, is small). We compare both expansions to N-body simulations and find that the Gamma expansion yields a better overall match to the numerical results.

2 pages, Latex using newpasp.sty, 2 figures. To appear in the proceedings of the IGRAP meeting on "Clustering at high redshift" (Marseille, June 1999)