Constraining Ω with Cluster Evolution

We show that the evolution of the number density of rich clusters of galaxiesbreaks the degeneracy between Omega (the mass density ratio of the universe)and sigma_{8} (the normalization of the power spectrum), sigma_{8}Omega^{0.5}\simeq 0.5, that follows from the observed present-day abundance of richclusters. The evolution of high-mass (Coma-like) clusters is strong in Omega=1,low-sigma_{8} models (such as the standard biased CDM model with sigma_{8}\simeq 0.5), where the number density of clusters decreases by a factor of \sim10^{3} from z = 0 to z \simeq 0.5; the same clusters show only mild evolutionin low-Omega, high-sigma_{8} models, where the decrease is a factor of \sim 10.This diagnostic provides a most powerful constraint on Omega. Usingobservations of clusters to z \simeq 0.5-1, we find only mild evolution in theobserved cluster abundance. We find Omega = 0.3 \pm 0.1 and sigma_{8} = 0.85\pm 0.15 (for Lambda = 0 models; for Omega + Lambda = 1 models, Omega = 0.34\pm 0.13). These results imply, if confirmed by future surveys, that we live ina low-den sity, low-bias universe.Comment: 14 pages, 3 Postscript figures, ApJ Letters, accepte