Non Gaussian extrema counts for CMB maps

TL;DR

This paper develops analytical and numerical methods to analyze the counts of extrema in weakly non-Gaussian CMB maps, aiding the detection of non-Gaussian features in cosmological data.

Contribution

It introduces second-order analytical expressions and a Monte Carlo approach for extrema counts in non-Gaussian CMB maps, enhancing analysis tools for cosmological studies.

Findings

Analytic expressions for extrema counts to second order in non-Gaussianity.

Monte Carlo method for arbitrary order computations.

Application to Planck data demonstrates effectiveness.

Abstract

In the context of the geometrical analysis of weakly non Gaussian CMB maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments expansion of the joint probability distribution of an isotropic random field, its gradient and invariants of the Hessian. Analytic expressions for these counts are given to second order in the non Gaussian correction, while a Monte Carlo method to compute them to arbitrary order is presented. Matching count statistics to these estimators is illustrated on fiducial non-Gaussian "Planck" data.