Extreme value statistics of weak lensing shear peak counts

Abstract

The statistics of peaks in weak gravitational lensingmaps is a promising technique to constrain cosmological parameters in present and future surveys. Here we investigate its power when using general extreme value statistics which is very sensitive to the exponential tail of the halo mass function. To this end, we use an analytic method to quantify the number of weak lensing peaks caused by galaxy clusters, large-scale structures and observational noise. Doing so, we further improve the method in the regime of high signal-to-noise ratios dominated by non-linear structures by accounting for the embedding of those counts into the surrounding shear caused by large-scale structures.We derive the extreme value and order statistics for both overdensities (positive peaks) and underdensities (negative peaks) and provide an optimized criterion to split a wide field survey into subfields in order to sample the distribution of extreme values such that the expected objects causing the largest signals are mostly due to galaxy clusters. We find good agreement of our model predictions with a ray-tracing N-body simulation. For a Euclid-like survey, we find tight constraints on σ8 and Ωm with relative uncertainties of ~10-3. In contrast, the equation of state parameter w0 can be constrained only with a 10 per cent level, and wa is out of reach even if we include redshift information.