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Session 95 - Cosmological Parameters and Large Scale Structure Formation.
Oral session, Friday, January 09
International Ballroom Center,
We present a method for determining the rms mass fluctuations on 8 h^-1Mpc scale, \sigma_8. The method utilizes the rate of evolution of the abundance of rich clusters of galaxies. Using the Press-Schechter approximation, we show that the cluster abundance evolution is a strong function of \sigma_8: d\log n/dz \propto -1/\sigma_8^2; low \sigma_8 models evolve exponentially faster than high \sigma_8 models, for a given mass cluster. For example, the number density of Coma-like clusters decreases by a factor of \sim 10^3 from z = 0 to z \simeq 0.5 for \sigma_8=0.5 models, while the decrease is only a factor of \sim 5 for \sigma_8 \simeq 1. The strong exponential dependence on \sigma_8 arises because clusters represent rarer density peaks in low \sigma_8 models. We show that the evolution rate at z \lesssim 1 is insensitive to the density parameter Ømega or to the exact shape of the power spectrum. Cluster evolution therefore provides a powerful constraint on \sigma_8. Using available cluster data to z \sim 0.8, we find \sigma_8 = 0.83 \pm 0.15. This amplitude implies a bias parameter b \simeq \sigma_8^-1 = 1.2 \pm 0.2, i.e., a nearly unbiased universe with mass approximately tracing light on large scales.
