Probability Distribution Function of Cosmological Density Fluctuations from Gaussian Initial Condition: Comparison of One- and Two-point Log-normal Model Predictions with N-body Simulations

摘要

We quantitatively study the probability distribution function (PDF) ofcosmological nonlinear density fluctuations from N-body simulations withGaussian initial condition. In particular, we examine the validity andlimitations of one-point and two-point log-normal PDF models against thosedirectly estimated from the simulations. We find that the one-point log-normalPDF describes very accurately the cosmological density distribution even in thenonlinear regime (the rms variance sigma_{nl} simlt 4 and the over-densitydelta simlt 100). Furthermore the two-point log-normal PDFs are also in goodagreement with the simulation data from linear to fairly nonlinear regime,while slightly deviate from them for delta simlt -0.5. Thus the log-normalPDF can be used as a useful empirical model for the cosmological densityfluctuations. While this conclusion is fairly insensitive to the shape of theunderlying power spectrum of density fluctuations P(k), models with substantialpower on large scales, i.e., nequiv dln P(k)/d ln k simlt -1, are betterdescribed by the log-normal PDF. On the other hand, we note that the one-to-onemapping of the initial and the evolved density fields consistent with thelog-normal model does not approximate the broad distribution of their mutualcorrelation even on average. Thus the origin of the phenomenological log-normalPDF approximation still remains to be understood.