A Deficiency of High-Redshift, Luminous X-Ray Clusters: Implications for the Fate of the Universe

From Press-Schechter formalism and the observed X-ray cluster L-T relation, we derive an X-ray cluster luminosity function that can be applied to the growing number of high-redshift, X-ray cluster luminosity catalogs to constrain cosmological parameters. In this paper, we apply this luminosity function to the Einstein Medium Sensitivity Survey (EMSS) to constrain Omega_0. Our results favor high values of this parameter: values that are consistent with unity. In the case of the EMSS, we find a deficiency of high-redshift, luminous X-ray clusters, which demonstrates that the luminosity function appears to have evolved above L_star. For the typical value of the slope of CDM-like mass density fluctuation power spectra on cluster scales (n = -1), we find that Omega_0 > 0.70 at the 84% confidence level and that Omega_0 > 0.33 at the 98% confidence level. We additionally apply a simplified version of this luminosity function to the published luminosity function of the ROSAT Brightest Cluster Survey to better constrain n. In combination with our EMSS results, our fitted value of n again favors high values of Omega_0. We do not assume any particular value of sigma_8