Constraining Ω with Cluster Evolution

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Abstract
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), σ8Ω0.5 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.
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