Quantifying the rareness of extreme galaxy clusters

TL;DR

This paper critiques the common bias in quantifying the rareness of extreme galaxy clusters, proposes unbiased measures, and demonstrates that, accounting for uncertainties, observed clusters are consistent with LambdaCDM.

Contribution

It identifies bias in existing methods, introduces unbiased measures for cluster rareness, and generalizes these to multiple clusters, improving the assessment of cosmological models.

Findings

Common bias can lead to false tension claims with LambdaCDM.

Unbiased measures show no tension when uncertainties are considered.

Application to non-Gaussian perturbations demonstrates the method's versatility.

Abstract

I show that the most common method of quantifying the likelihood that an extreme galaxy cluster could exist is biased and can result in false claims of tension with LambdaCDM. This common method uses the probability that at least one cluster could exist above the mass and redshift of an observed cluster. I demonstrate the existence of the bias using sample cluster populations, describe its origin and explain how to remove it. I then suggest potentially more suitable and unbiased measures of the rareness of individual clusters. Each different measure will be most sensitive to different possible types of new physics. I show how to generalise these measures to quantify the total `rareness' of a set of clusters. It is seen that, when mass uncertainties are marginalised over, there is no tension between the standard LambdaCDM cosmological model and the existence of any observed set of clusters. As a case study, I apply these rareness measures to sample cluster populations generated using primordial density perturbations with a non-Gaussian spectrum.