The evolution of X-ray galaxy clusters as a constraint of Omega(0)

Clusters of galaxies are rare objects and as such, their properties are particularly sensitive to the underlying density fluctuations. Therefore, the cluster population provides very stringent constraints on models of galaxy formation. We here show how self-consistent modeling of X-ray galaxy dusters can be used to constrain the power spectrum of the initial density perturbations assumed to seed galaxy formation. We also demonstrate that the combined knowledge of the redshift distribution of X-ray selected galaxy clusters and that of the X-ray luminosity-temperature correlation at high redshifts offers a powerful method to constrain the mean density of the universe. Considering its large effective area SODART aboard SPECTRUM-RG is extremely well suited to temperature measurement of distant clusters and the Ohm(0) test we propose is well within the capabilities of the near future X-ray telescopes.