Testing cosmological models with clusters of galaxies

Galaxy clusters are ideal probes for the large-scale structure of the Universe and for the tests of cosmological models. We use, REFLEX, the currently largest and best defined cluster X-ray survey to illustrate this application of galaxy cluster studies. Based on this survey of X-ray selected clusters of galaxies we determine statistical properties of the galaxy cluster population, their spatial correlation, and the density fluctuation power spectrum of the cosmic matter distribution on large scales up to about 1 Gpc. Comparing these results with predictions of cosmological models we obtain tight constrains for the matter density parameter of the Universe, consistent with the combined results from observations of the microwave background anisotropies and distant type la supernovae. The only difference between the present results and the "concordance model" is a low value for the as-normalization. Exploring the parameter space of the cosmic matter density and the equation of state parameter of dark energy most favoured by the combined observations of REFLEX clusters and distant type Ia supernovae we find that the conventional cosmological constant model is best consistent with the observational data.