Constraining Omega with Cluster Evolution

Neta A. Bahcall, Xiaohui Fan, Renyue Cen

Published 1997-06-03Version 1

We show that the evolution of the number density of rich clusters of galaxies breaks 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 rich clusters. 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 \sim 10^{3} from z = 0 to z \simeq 0.5; the same clusters show only mild evolution in low-Omega, high-sigma_{8} models, where the decrease is a factor of \sim 10. This diagnostic provides a most powerful constraint on Omega. Using observations of clusters to z \simeq 0.5-1, we find only mild evolution in the observed 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 in a low-den sity, low-bias universe.