Evolution of the Cosmological Density Distribution Function: A New Analytical Model

The one-point probability distribution function (pdf) of the large-scale density field is an important tool to follow the evolution of cosmological structures. In this paper we present a new model for this pdf for all regimes and all densities, that is from linear to highly non-linear scales and from rare voids up to rare high densities. This is probably the simplest model one can build which is consistent with normalization constraints and known rigorous results (the quasi-linear regime and the rare void limit). It is fully parameterized by the non-linear variance and skewness. We obtain a good agreement with N-body data from realistic cosmological simulations of the VIRGO consortium and we find that it works significantly better than previous models such as the lognormal model or the Extended Perturbation Theory (EPT). We explain this success as a result of the tight constraints onto the pdf provided by these consistency conditions. We also point out that while the Lagrangian dynamics of typical fluctuations is quite complex the statistical outcome seems rather simple. This simple model should be useful for studies which require a realistic and convenient description of this pdf.