NON-GAUSSIAN SIGNATURES FROM GAUSSIAN INITIAL FLUCTUATIONS - EVOLUTION OF SKEWNESS AND KURTOSIS FROM COSMOLOGICAL SIMULATIONS IN THE HIGHLY NONLINEAR REGIME

Following recent observational studies of counts-in-cells statistic, we consider the evolution of the third and fourth moments of distribution functions of the density contrast 6. We define a normalized skewness as S = [delta3]/[delta2]2 and a normalized kurtosis as K = ([delta4] - 3 [delta2]2)/[delta2]3, which are expected from previous theoretical and phenomenological arguments to be '' constants '' in the mildly nonlinear regime. We extended the study of S and K into the highly nonlinear regime 1 less than or similar to delta(rms) = [delta2]1/2 less than or similar to 30 using N-body simulations and taking into account the effect of Poisson shot noise. We find that the simple scaling relation which holds in the mildly nonlinear regime breaks down in the highly nonlinear regime. Both S and K exhibit variation which strongly depends on the primordial power spectrum of density fluctuations, but only weakly on the epoch. For a low-density (OMEGA = 0.2; lambda = 0.8) cold dark matter model at the ''present epoch,'' the normalized skewness and kurtosis in cubic cells are well approximated by S(F) almost-equal-to 3 delta(rms)0.4 and K(F) almost-equal-to 15 delta(rms)0.9 (after removing the shot-noise contribution), over the range 1 less than or similar to delta(rms) less than or similar to 27. For a simulation with initial white-noise spectrum the moments vary more slowly, S(F) almost-equal-to 2 delta(rms)0.2 and K(F) almost-equal-to 8 delta(rms)0.3. Our present findings are in conflict with simple hierarchical clustering models with a power-law correlation function which predict that S(F) and K(F) are independent of the scale. Furthermore, we find that in redshift space the moments, as well as S and K, are smaller than in real space for delta(rms) > 1. Consequently S and S(F) appear to be '' constants '' in redshift space analysis which might explain several observational indications in favor of hierarchical clustering models. We also discuss sparse sampling and the effect of filtering scale and shape. Counts-in-cells of IRAS and optical galaxies suggest S approximately 2 for delta(rms) less than or similar to 1, while from the correlation functions of optical galaxies S approximately 4 for delta(rms) greater than or similar to 1. These values are in accord with that expected from gravitational clustering from Gaussian initial conditions and may carry important information on the shape of the power spectrum.