EVOLUTION OF ONE-POINT DISTRIBUTIONS FROM GAUSSIAN INITIAL FLUCTUATIONS

We study the quasi-linear evolution of the one-point probability densi ty functions (PDFs) of the smoothed density and velocity fields in a c osmological gravitating system beginning with Gaussian initial fluctua tions. Our analytic results are based on the Zel'dovich approximation and laminar flow. A numerical analysis extends the results into the mu ltistreaming regime using the smoothed fields of a CDM N-body simulati on. We find that the PDF of velocity, both Lagrangian and Eulerian, re mains Gaussian under the laminar Zel'dovich approximation, and it is a lmost indistinguishable from Gaussian in the simulations. The PDF of m ass density deviates from a normal distribution early in the quasi-lin ear regime and it develops a shape remarkably similar to a lognormal d istribution with one parameter, the rms density fluctuation sigma. App lying these results to currently available data we find that the PDFs of the velocity and density fields, as recovered by the POTENT procedu re from observed velocities assuming OMEGA = 1, or as deduced from a r edshift survey of IRAS galaxies assuming that galaxies trace mass, are consistent with Gaussian initial fluctuations.