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 will overestimate the confidence level at
which Lambda-CDM 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
2-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.
