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

P. Fosalba·E. Gaztanaga·E. Elizalde
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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, $σ^2$, 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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P. Fosalba, E. Gaztanaga, E. Elizalde. 1999-10-18. Gravitational Evolution of the Large-Scale Density Distribution: The Edgeworth & Gamma Expansions. https://arxiv.org/abs/astro-ph/9910308

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