A measurement of the density parameter derived from the evolution of cluster X-ray temperatures

We have, for the first time, determined the cluster X-ray temperature function at a redshift other than zero. The observed evolution of the temperatures is mild to a redshift of one-third. The normalization of the luminosity-temperature relation is 0.92 +/- 0.07 of the low-redshift relation (1 sigma error), assuming that its shape is the same. Such behavior occurs when clusters form with constant central entropy. The evolution of the temperature function implies that Omega(0), is 0.50 +/- 0.14 assuming an open universe, or 0.55 +/- 0.17 assuming that a cosmological constant produces a flat universe (1 sigma symmetrized errors). A closed universe, Omega(0) greater than or equal to 1, is excluded at greater than 99% confidence. The amplitude of the mass density fluctuations averaged over 8 h(-1) Mpc spheres, sigma(8), is 0.66=(+0.22)(-0.08) and 0.66(-0.17)(+0.34) (1 sigma errors) for the open and flat models, respectively.