Quantifying the rareness of extreme galaxy clusters

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 ΛCDM. 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 ΛCDM 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