THE SKEWNESS AND KURTOSIS OF THE PROJECTED DENSITY DISTRIBUTION FUNCTION - VALIDITY OF PERTURBATION-THEORY

We study the domain of validity of Perturbation Theory (PT), by compar ing its predictions for the reduced skewness, s(3), and kurtosis, s(4) , Of the projected cosmological density field, with the results of N-b ody simulations. We investigate models with different linear power spe ctra and consider as physical applications both angular galaxy catalog ues and weak lensing surveys. We first find that the small-angle appro ximation for the predicted skewness provides a good match to the exact numerical PT results. On the other hand, results from non-linear simu lated catalogues agree well with PT results on quasi-linear angular sc ales, which correspond to scales larger than about 1 deg in the applic ations we have considered. We also point out that projection effects t end to attenuate the effects of strong non-linearities in the angular skewness and kurtosis.