2010MNRAS.405..681F

We computed the power spectrum of weak cosmic shear in models with non-Gaussian primordial density fluctuations. Cosmological initial conditions deviating from Gaussianity have recently attracted much attention in the literature, especially with respect to their effect on the formation of non-linear structures and because of the bounds that they can put on the inflationary epoch. The fully non-linear matter power spectrum was evaluated with the use of the physically motivated, semi-analytic halo model, where the mass function and linear halo bias were suitably corrected for non-Gaussian cosmologies. In agreement with previous work, we found that a level of non-Gaussianity compatible with cosmic microwave background bounds and with positive skewness produces an increase in power of the order of a few per cent at intermediate scales. We then used the matter power spectrum, together with observationally motivated background source redshift distributions in order to compute the cosmological weak-lensing power spectrum. We found that the degree of deviation from the power spectrum of the reference Gaussian model is small compared to the statistical error expected from even future weak-lensing surveys. However, summing the signal over a large range of multipoles can beat down the noise, bringing to a significant detection of non-Gaussianity at the level of few tens, when all other cosmological parameters are held fixed. Finally, we have shown that the constraints on the level of non-Gaussianity can be improved by ∼ 20 per cent with the use of weak-lensing tomography.