Probability distribution function of cosmological density fluctuations from a Gaussian initial condition: Comparison of one-point and two-point lognormal model predictions with N-body simulations

We quantitatively study the probability distribution function (PDF) of cosm ological nonlinear density fluctuations from N-body simulations with a Gaus sian initial condition. In particular, we examine the validity and limitati ons of one-point and two-point lognormal PDF models against those directly estimated from the simulations. We find that the one-point lognormal PDF ve ry accurately describes the cosmological density distribution even in the n onlinear regime (rms variance sigma nl less than or similar to 4, overdensi ty delta less than or similar to 100). Furthermore, the two-point lognormal PDFs are also in good agreement with the simulation data from linear to fa irly nonlinear regimes, while they deviate slightly from the simulation dat a for delta less than or similar to -0.5. Thus, the lognormal PDF can be us ed as a useful empirical model for the cosmological density fluctuations. W hile this conclusion is fairly insensitive to the shape of the underlying p ower spectrum of density fluctuations P(k), models with substantial power o n large scales, i.e., n = d ln P(k)/d ln k less than or similar to -1, are better described by the lognormal PDF. On the other hand, we note that the one-to-one mapping of the initial and evolved density fields, consistent wi th the lognormal model, does not approximate the broad distribution of thei r mutual correlation even on average. Thus, the origin of the phenomenologi cal lognormal PDF approximation still remains to be understood.