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 par ticularly 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 duster s can be used to constrain the power spectrum of the initial density pertur bations assumed to seed galaxy formation. We also demonstrate that the comb ined knowledge of the redshift distribution of X-ray selected galaxy cluste rs and that of the X-ray luminosity-temperature correlation at high redshif ts 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 te lescopes.