Testing cosmology with extreme galaxy clusters

Motivated by recent suggestions that a number of observed galaxy clusters have masses which are too high for their given redshift to occur naturally in a standard model cosmology, we use extreme value statistics to construct confidence regions in the mass-redshift plane for the most extreme objects expected in the universe. We show how such a diagram not only provides a way of potentially ruling out the concordance cosmology, but also allows us to differentiate between alternative models of enhanced structure formation. We compare our theoretical prediction with observations, placing currently observed high-and low-redshift clusters on a mass-redshift diagram, and find - provided we consider the full sky to avoid a posteriori selection effects - that none is in significant tension with concordance cosmology.