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 comparing its predictions for the reduced skewness, s₃, and kurtosis, S₄, of the projected cosmological density field, with the results of N-body simulations. We investigate models with different linear power spectra and consider as physical applications both angular galaxy catalogues and weak lensing surveys. We first find that the small-angle approximation for the predicted skewness provides a good match to the exact numerical PT results. On the other hand, results from non-linear simulated catalogues agree well with PT results on quasi-linear angular scales, which correspond to scales larger than about 1 deg in the applications we have considered. We also point out that projection effects tend to attenuate the effects of strong non-linearities in the angular skewness and kurtosis.