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.Comment: 14 pages, 3 Postscript figures, ApJ Letters, accepte