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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.
Coles et al. (Mon,) studied this question.