Probability Distribution Function of Cosmological Density Fluctuations from a Gaussian Initial Condition: Comparison of One‐Point and Two‐Point Lognormal Model Predictions withN‐Body Simulations

We quantitatively study the probability distribution function (PDF) of cosmological nonlinear density fluctuations from N-body simulations with Gaussian initial condition. In particular, we examine the validity and limitations of one-point and two-point log-normal PDF models against those directly estimated from the simulations. We find that the one-point log-normal PDF describes very accurately the cosmological density distribution even in the nonlinear regime (the rms variance ₍₋ 4 and the over-density 100). Furthermore the two-point log-normal PDFs are also in good agreement with the simulation data from linear to fairly nonlinear regime, while slightly deviate from them for -0. 5. Thus the log-normal PDF can be used as a useful empirical model for the cosmological density fluctuations. While this conclusion is fairly insensitive to the shape of the underlying power spectrum of density fluctuations P (k), models with substantial power on large scales, i. e. , n d P (k) /d k -1, are better described by the log-normal PDF. On the other hand, we note that the one-to-one mapping of the initial and the evolved density fields consistent with the log-normal model does not approximate the broad distribution of their mutual correlation even on average. Thus the origin of the phenomenological log-normal PDF approximation still remains to be understood.