Kurtosis as a Non--Gaussian Signature of the Large--Scale Velocity Field

Abstract

We discuss the non--linear growth of the kurtosis of the smoothed peculiar velocity field (along an arbitrary direction), in an Einstein--de Sitter universe, induced by Gaussian primordial density fluctuations. Applying the perturbative theory, we show that, for different cosmological models, a departure from the original Gaussian distribution is gravitationally induced only on small scales ($\simlt 20-30$ Mpc). Models with scale--free power spectrum $P(k)\propto k^n$, with $-1<n\le 1$, are also considered. When the fluid particles move according to the Zel'dovich approximation the probability distribution of the peculiar velocity field remains unaltered during the evolution.

10 pages in Latex (plus 2 figures in a separate file), PD-cosmo/9401

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