Cosmic shear and halo abundances: analytical versus numerical results

The aperture mass has been shown in a series of recent publications to be a useful quantitative tool for weak lensing studies, ranging from cosmic she ar to the detection of a mass-selected sample of dark matter haloes. Quanti tative analytical predictions for the aperture mass have been based on a nu mber of simplifying assumptions. In this paper, we test the reliability of these assumptions and the quality of the analytic approximations, using ray -tracing simulations through a cosmological density field generated by very large N-body simulations. We find that those analytic predictions which ta ke into account the non-linear evolution of the matter distribution, such a s the dispersion of the aperture mass and the halo abundance, are surprisin gly accurately reproduced with our numerical results, whereas the predictio ns for the skewness, based on quasi-linear theory, are rather imprecise. In particular, we verify numerically that the probability distribution of the aperture mass decreases exponentially for values much larger than the rms. Given the good overall agreement, comparisons between the observed distrib ution of the aperture mass and the theoretical values provide a powerful to ol for testing cosmological models.