Extreme value statistics of the weak lensing convergence: 1. primordial non-Gaussianities

TL;DR

This paper develops an analytical framework using extreme value statistics to constrain inflationary non-Gaussianities from weak lensing convergence data, with applications to the EUCLID survey.

Contribution

It introduces a novel analytical approach linking extreme value statistics of weak lensing convergence to inflationary non-Gaussianity parameters, enabling parameter constraints from observational data.

Findings

Analytical expressions for the extreme value distribution are derived.

Extreme value statistics can constrain fnl and gnl parameters from weak lensing data.

The method is applicable to upcoming surveys like EUCLID for inflationary model testing.

Abstract

The subject of this paper is the investigation of inflationary non-Gaussianities of the local type with extreme value statistics of the weak lensing convergence kappa. Specifically, we describe the influence of inflationary non-Gaussianities parameterised by fnl and gnl on the probability distribution p(kappa)dkappa of the smoothed convergence field with a Gram-Charlier series, for which we compute the cumulants kappa_n of the smoothed convergence field as a configuration space average of the weak convergence polyspectra. We derive analytical expressions for the extreme value distribution and show that they correspond very well to direct samples of extreme values from the Gram-Charlier distribution. We show how the standard Gumbel distribution for the extreme values is recovered in the limit of large sample size. We investigate the shape and position of the extreme value distribution for fnl- and gnl-type non-Gaussianity and quantify the dependence on the number of available samples, leading to the inference of non-Gaussianity parameters from observed extreme values. From the observation of single extreme values in the EUCLID weak lensing survey is is possible to place constraints on fnl and gnl of the order 10^2 and 10^5, respectively, while tnl can not be constrained in a meaningful way.