Measuring Cosmological Parameters from the Evolution of Cluster X-ray Temperatures

We have determined the cluster X-ray temperature function from two flux- and redshift-limited samples of clusters. The first sample is comprised of 25 clusters with average redshift 0.05. The local temperature function derived from it supercedes the one we previously published. Fourteen clusters with average redshift 0.38 comprise the second sample. We perform maximum likelihood fits of cluster evolution models to these data in order to constrain cosmological parameters. For an open model with zero cosmological constant we find that the density parameter is Omega_0 = 0.49+/-0.12, the rms mass density fluctuation averaged over 8 h-1 Mpc spheres is sigma_8 = 0.72+/-0.10, and the effective index of the mass density fluctuation spectrum on cluster scales is n = -(1.72+/-0.34) where all errors are symmetrized at 68% confidence. The corresponding results for the case where a cosmological constant produces a flat universe are : 0.44+/-0.12, 0.77+/-0.15, and -(1.68+/-0.38). These results agree with those determined from a variety of different independent methods, including supernovae, galaxy-galaxy correlations, fluctuations in the microwave background, gravitational lens statistics, and cluster peculiar velocities.