Cosmological Parameter Estimation with the Galaxy Cluster Abundance

Clusters of galaxies are the most massive virialized structures in the Universe. Given that the mass function of large-scale structures decreases exponentially at the high-mass end, galaxy clusters are a sensitive probe of its normalization and redshift evolution, and hence of the cosmological parameters that most influence it. It will be discussed to what extent these cosmological parameters, namely the present amplitude of density perturbations, the matter density and a possible cosmological constant, can be constrained using observational data on the present and past abundance of galaxy clusters. Results will be presented based on the available data, as well as expected constraints from the X-ray Cluster Survey (XCS).