Testing Cosmological Models with the Properties of the Galaxy Cluster Population

Galaxy clusters, as the largest well defined objects in our Universe, form an integral part of the cosmic large-scale structure. Their formation and evolution is therefore tightly coupled to the evolution of the Universe as a whole, which makes clusters important probes to test cosmological models. Both, the cluster abundance quantified by the mass function and the cluster spatial distribution can be used as sensitive probes to constrain cosmological parameters. This use of galaxy clusters is illustrated by means of the X-ray detected galaxy cluster samples from the ROSAT All-Sky Survey. One of the current limitations of using galaxy clusters for cosmological tests is the uncertain link between observable cluster properties with the cluster mass, which enters cosmological modeling. Large progress has been made recently, however, in understanding the statistics of galaxy cluster structure and the scaling relations between cluster observables and cluster gravitational mass in particular for X-ray observations. Progress has also been made in extending the redshift range of cluster studies to redshifts up to z = 1.6. If we are provided with better statistics from much larger galaxy cluster samples over this redshift range, interesting constraints will be obtained on the nature of Dark Energy or on the possibility that more unconventional cosmological models apply to our Universe. The scope of the eROSITA Satellite Mission, with a launch as early as 2012, is tailored to provide the basis for this goal with an expected number of galaxy clusters detected in X-rays of the order of 100 000. Other survey missions at different wavelengths will complement this effort as well, making galaxy cluster cosmology and important research field in the next decade.