Constraining with Cluster Evolution

We show that the evolution of the number density of rich clusters of galaxies breaks the degeneracy between (the mass density ratio of the universe) and 8 (the normalization of the power spectrum), 8 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 = 1, low-8 models (such as the standard biased CDM model with 8 ' 0:5), where the number density of clusters decreases by a factor of 10 3 from z = 0 to z ' 0:5; the same clusters show only mild evolution in low-, high-8 models, where the decrease is a factor of 10. This diagnostic provides a most powerful constraint on. Using observations of clusters to z ' 0:5 ? 1, we nd only mild evolution in the observed cluster abundance. We nd = 0:3 0:1 and 8 = 0:85 0:15 (for = 0 models; for + = 1 models, = 0:34 0:13). These results imply, if connrmed by future surveys, that we live in a low-density, low-bias universe.