Primordial Non-Gaussianity and Extreme-Value Statistics of Galaxy Clusters

TL;DR

This paper develops a statistical framework using Extreme-Value Statistics to assess the likelihood of observing the most massive galaxy clusters in surveys, accounting for primordial non-Gaussianity effects on their distribution.

Contribution

It introduces a method to incorporate primordial non-Gaussianity into extreme-value statistics for galaxy clusters, improving predictions of their maximum masses in surveys.

Findings

Primordial non-Gaussianity shifts the peak of the extreme-mass cluster distribution.

The correction for non-Gaussianity is significant for f_NL > 100 in large surveys.

The existence of a high-redshift cluster is consistent with Gaussian initial conditions.

Abstract

What is the size of the most massive object one expects to find in a survey of a given volume? In this paper, we present a solution to this problem using Extreme-Value Statistics, taking into account primordial non-Gaussianity and its effects on the abundance and the clustering of rare objects. We calculate the probability density function (pdf) of extreme-mass clusters in a survey volume, and show how primordial non-Gaussianity shifts the peak of this pdf. We also study the sensitivity of the extreme-value pdfs to changes in the mass functions, survey volume, redshift coverage and the normalization of the matter power spectrum, {\sigma}_8. For 'local' non-Gaussianity parametrized by f_NL, our correction for the extreme-value pdf due to the bias is important when f_NL > O(100), and becomes more significant for wider and deeper surveys. Applying our formalism to the massive high-redshift cluster XMMUJ0044.0-2-33, we find that its existence is consistent with f_NL = 0, although the conclusion is sensitive to the assumed values of the survey area and {\sigma}_8. We also discuss the convergence of the extreme-value distribution to one of the three possible asymptotic forms, and argue that the convergence is insensitive to the presence of non-Gaussianity.