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

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

1999-10-18

arxiv.org/abs/astro-ph/9910308v1

Astronomy and Astrophysics

Astrophysics

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

Scientific paper

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.

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