Constraining Ω with Cluster Evolution

We show that the evolution of the number density of rich clusters of galaxies breaks the degeneracy between Ω (the mass density ratio of the universe) and σ₈ (the normalization of the power spectrum), σ₈Ω^0.5 ≃ 0.5, that follows from the observed present-day abundance of rich clusters. The evolution of high-mass (Coma-like) clusters is strong in Ω = 1, low-σ₈ models (such as the standard biased cold dark matter model with σ₈ ≃ 0.5), where the number density of clusters decreases by a factor of about 10³ from z = 0 to z ≃ 0.5; the same clusters show only mild evolution in low-Ω, high-σ₈ models, where the decrease is a factor of about 10. This diagnostic provides a most powerful constraint on Ω. Using observations of clusters to z ≃ 0.5-1, we find only mild evolution in the observed cluster abundance. We find Ω = 0.3 ± 0.1 and σ₈ = 0.85 ± 0.15 (for Λ = 0 models; for Ω + Λ = 1 models, Ω = 0.34 ± 0.13). These results imply, if confirmed by future surveys, that we live in a low-density, low-bias universe.