WHAT DOES CLUSTER REDSHIFT EVOLUTION REVEAL

Evolution of the cluster population has been recognized as a powerful cosmological tool. While the present-day abundance of X-ray clusters i s degenerate in sigma(8), n and Omega(0), Oukbir and Blanchard (1992, 1997) have pointed out that the number density evolution of X-ray clus ters with redshift can be used to determine Omega(0). Here, we clarify the origin of this statement by identifying those parameters to which the evolution of cluster number density is most sensitive. We find th at the evolution is controlled by only two parameters: the amplitude o f fluctuations, sigma(M), on the scale associated with the mass under consideration, R = 9.5h(1/3)Omega(0)(-1/3) M-15(1/3) h(-1)Mpc, and the cosmological background density, Omega(0). In contrast, evolution is remarkably insensitive to the slope of the power spectrum. We verify t hat the number density evolution of clusters is a powerful probe of th e mean density of the universe, under the condition that sigma(M) is c hosen to reproduce current-day abundances. Comparison of the cluster a bundance at z similar to 0.5 - 0.6, from the EMSS, to the present-day abundance, from the ROSAT BCS sample, unambiguously reveals the existe nce of significant negative evolution. This number evolution, in conju nction with the absence of any negative evolution in the luminosity-te mperature relation, provides robust evidence in favor of a critical de nsity universe (Omega(0) = 1), in agreement with the analysis by Sadat et al. (1998).