The mean density of the Universe from cluster evolution

The determination of the mean density of the Universe is a long standing problem of modern cosmology. The number density evolution of x-ray clusters at a fixed temperature is a powerful cosmological test, new in nature (Oukbir and Blanchard, 1992), somewhat different from standard analyses based on the dynamical measurement of individual objects. However, the absence of any available sample of x-ray selected clusters with measured temperatures at high redshift has prevented this test from being applied earlier. Recently, temperature measurements of ten EMSS clusters at $0.3 \le z \le 0.4$ have allowed the application of this test (Henry, 1997). In this work, we present the first results of a new analysis we have performed of this data set as well as a new estimation of the local temperature distribution function of clusters: a likelihood analysis of the temperature distribution functions gives a preferred value for the mean density of the universe which corresponds to 75% of the critical density. An open model with a density smaller than 30% of the critical density is rejected with a level of significance of 95%.