Extreme value statistics of weak lensing shear peak counts

TL;DR

This paper develops an analytic framework using extreme value statistics to analyze weak lensing shear peak counts, providing improved predictions and constraints on cosmological parameters for large surveys like Euclid.

Contribution

It introduces an analytic method for extreme value analysis of shear peaks, accounting for non-linear structures and embedding effects, enhancing cosmological parameter estimation.

Findings

Model predictions agree with ray-tracing simulations.

Tight constraints on σ8 and Ωm with Euclid-like surveys.

Limited constraints on dark energy parameters w0 and wa.

Abstract

The statistics of peaks in weak gravitational lensing maps 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 over-densities (positive peaks) and under-densities (negative peaks) and provide an optimized criterion to split a wide field survey into sub-fields 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 $\sigma_8$ and $\Omega_\text{m}$ with relative uncertainties of $\sim 10^{-3}$. In contrast, the equation of state parameter $w_0$ can be constrained only with a $10\%$ level, and $w_\text{a}$ is out of reach even if we include redshift information.