A Consistent Approach to Falsifying Lambda-CDM with Rare Galaxy Clusters
We consider methods with which to answer the question "is any observed galaxy cluster too unusual for Lambda-CDM?" After emphasising that many previous attempts to answer this question have fallen foul of a statistical bias which causes them to overestimate the confidence levels to which Lambda-CDM can be ruled out, we outline a consistent approach to these rare clusters which allows the question to be answered. We explicitly separate the two procedures of first ranking clusters according to which appears 'most unusual' and secondly calculating the probability that such an unusual observation was made in a given cosmology. For the ranking procedure we define three properties of individual galaxy clusters, each of which are sensitive to changes in cluster populations arising from different modifications to the cosmological model. We use these properties to define the "equivalent mass at redshift zero" for a cluster - the mass of an equally unusual cluster today. This quantity is independent of the observational survey in which the cluster was found, which makes it an ideal proxy for ranking the relative unusualness of clusters detected by different surveys. We then calculate the probability that any cluster could have been observed with this equivalent mass at redshift zero, avoiding the a posteriori bias present in many earlier analyses. These two steps are performed for a systematic and comprehensive sample of observed galaxy clusters and we confirm that none are more than 1-sigma deviations from the Lambda-CDM expectation. Whereas we have only applied our method to galaxy clusters, it is applicable to any isolated, collapsed, halo. As motivation for future surveys, we also calculate where in the mass redshift plane the rarest halo is most likely to be found, giving information as to which objects might be the most fruitful in the search for new physics.