On the estimation of gravity‐induced non‐Gaussianities from weak‐lensing surveys

We study various measures of weak‐lensing distortions in future surveys, taking into account the noise arising from the finite survey size and the intrinsic ellipticity of galaxies. We also consider a realistic redshift distribution of the sources, as expected for the SNAP mission. We focus on the low‐order moments and the full distribution function (PDF) of the aperture mass M ap and of the smoothed shear component γ i s . We also propose new unbiased estimators for low‐order cumulants which have less scatter than the usual estimators of non‐Gaussianity based on the moments themselves. Then, using an analytical model which has already been seen to provide a good description of weak gravitational lensing through a comparison with numerical simulations, we study the statistical measures that can be extracted from future surveys such as the SNAP experiment. We recover the fact that at small angular scales (1 < θ s < 10 arcmin) the variance can be extracted with an accuracy of a few per cent. Non‐Gaussianity can also be measured from the skewness of the aperture mass (at a 10 per cent level), while the shear kurtosis is more noisy and cannot be easily measured beyond 6 arcmin. On the other hand, we find that the PDF of the estimator associated with the aperture mass can be distinguished both from the Gaussian and the Edgeworth expansion and could provide useful constraints, while this appears to be difficult to realize with the shear component. Finally, we investigate various survey strategies and the possibility of performing a redshift binning of the sample.