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 are in significant tension with concordance cosmology.
