The non-Gaussian tail of cosmic-shear statistics

Due to gravitational instability, an initially Gaussian density field develops non-Gaussian features as the Universe evolves. The most prominent non-Gaussian features are massive haloes, visible as clusters of galaxies. The distortion of high-redshift galaxy images due to the tidal gravitational field of the large-scale matter distribution, called cosmic shear, can be used to investigate the statistical properties of the LSS. In particular, non-Gaussian properties of the LSS will lead to a non-Gaussian distribution of cosmic-shear statistics. The aperture mass ($M_{\rm ap}$) statistics, recently introduced as a measure for cosmic shear, is particularly well suited for measuring these non-Gaussian properties. In this paper we calculate the highly non-Gaussian tail of the aperture mass probability distribution, assuming Press-Schechter theory for the halo abundance and the `universal' density profile of haloes as obtained from numerical simulations. We find that for values of $M_{\rm ap}$ much larger than its dispersion, this probability distribution is closely approximated by an exponential, rather than a Gaussian. We determine the amplitude and shape of this exponential for various cosmological models and aperture sizes, and show that wide-field imaging surveys can be used to distinguish between some of the currently most popular cosmogonies. Our study here is complementary to earlier cosmic-shear investigations which focussed more on two-point statistical properties.