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A consistent approach to falsifying ΛCDM with rare galaxy clusters

We consider methods with which to answer the question ``is any observed galaxy cluster too unusual for ΛCDM?'' After emphasising that many previous attempts to answer this question will overestimate the confidence level at which ΛCDM can be ruled out, we outline a consistent approach to these rare clusters, which allows the question to be answered. We define three statistical measures, each of which are sensitive to changes in cluster populations arising from different modifications to the cosmological model. We also 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. These methods are then used on a comprehensive sample of observed galaxy clusters and we confirm that all are less than 2σ deviations from the ΛCDM 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.