The non‐Gaussian tail of cosmic‐shear statistics

Owing 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 because of the tidal gravitational field of the large‐scale matter distribution, called cosmic shear, can be used to investigate the statistical properties of the large‐scale structure (LSS). In particular, non‐Gaussian properties of the LSS will lead to a non‐Gaussian distribution of cosmic‐shear statistic. The aperture mass ( M 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 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 focused more on two‐ and three‐point statistical properties.