Testing cosmological models using relative mass-redshift abundance of SZ
  clusters
  Recent detection of high-redshift, massive clusters through
Sunyaev-Zel'dovich observations has opened up a new way to test cosmological
models. It is known that detection of a single supermassive cluster at a very
high redshift can rule out many cosmological models all together. However,
since dealing with different observational biases makes it difficult to test
the likeliness of the data assuming a cosmological model, most of the cluster
data (except those with high mass-redshift) stays untouched in confronting
cosmological models with cluster observations. We propose here that one can use
the relative abundance of the clusters with different masses at different
redshifts to test the likeliness of the data in the context of cosmological
models. For this purpose we propose a simple parametric form for the efficiency
of observing clusters at different mass-redshift and we test if the standard
LCDM model can explain the observed abundance of the clusters using this
efficiency parameterization. We argue that one cannot expect an unusual and
highly parametric form of the efficiency function to fit the observed data
assuming a theoretical model. Using many realizations of Monte Carlo
simulations we show that the standard spatially flat LCDM model is barely
consistent with the SPT cluster data using a simple and plausible
two-dimensional efficiency function for detection of the clusters. More cluster
data are needed to make any strong conclusion.
