Imprints of primordial non-Gaussianity on the number counts of cosmic shear peaks

We studied the effect of primordial non-Gaussianity with varied bispectrum shapes on the number counts of signal-to-noise ratio peaks in wide-field cosmic shear maps. The two cosmological contributions to this particular weak lensing statistic, namely the chance projection of Large Scale Structure (LSS) and the occurrence of real, cluster-sized dark matter haloes, have been modelled semianalytically, thus allowing to easily introduce the effect of non-Gaussian initial conditions. We performed a Fisher matrix analysis by taking into account the full covariance of the peak counts in order to forecast the joint constraints on the level of primordial non-Gaussianity and the amplitude of the matter power spectrum that are expected from future wide-field imaging surveys. We find that positive-skewed non-Gaussianity increases the number counts of cosmic shear peaks, more so at high signal-to-noise ratio values, where the signal is mostly dominated by massive clusters as expected. The increment is at the level of similar to 1 per cent for f(NL) = 10 and similar to 10 per cent for f(NL) = 100 for a local shape of the primordial bispectrum, while different bispectrum shapes give generically a smaller effect. For a future survey on the model of the proposed ESA space mission Euclid and by avoiding the strong assumption of being capable of distinguishing the weak-lensing signal of galaxy clusters from the chance projection of LSSs, we forecast a 1 sigma error on the level of non-Gaussianity of similar to 30-40 for the local and equilateral models, and of similar to 100-200 for the less explored enfolded and orthogonal bispectrum shapes.