Testing approximations for non-linear gravitational clustering

We investigate the accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the non-linear regime. We compare the results of the application of linear theory, the lognormal approximation and the Zeldovich approximation to a set of initial data with corresponding results obtained by a full three-dimensional N-body computation from the same initial conditions. A cross-correlation technique is used to quantify the agreement between approximated and N-body 'final' distributions for different initial power spectra, different normalization epochs and different degrees of smoothing of the final results. We also study the distribution function of mass density.