Density distribution of the cosmological matter field
  The one-point probability distribution function (PDF) of the matter density
field in the universe is a fundamental property that plays an essential role in
cosmology for estimates such as gravitational weak lensing, non-linear
clustering, massive production of mock galaxy catalogs, and testing predictions
of cosmological models. Here we make a comprehensive analysis of the dark
matter PDF using a suite of 7000 N-body simulations that covers a wide range of
numerical and cosmological parameters. We find that the PDF has a simple shape:
it declines with density as a power-law P~rho**(-2), which is exponentially
suppressed on both small and large densities. The proposed double-exponential
approximation provides an accurate fit to all our N-body results for small
filtering scales R< 5Mpc/h with rms density fluctuations sigma>1. In
combination with the spherical infall model that works well for small
fluctuations sigma<1, the PDF is now approximated with just few percent errors
over the range of twelve orders of magnitude -- a remarkable example of
precision cosmology. We find that at 5-10% level the PDF explicitly depends on
redshift (at fixed sigma) and on cosmological density parameter Omega_m. We
test different existing analytical approximations and find that the often used
log-normal approximation is always 3-5 times less accurate than either the
double-exponential approximation or the spherical infall model.
