The Most Massive Distant Clusters: Determining Ω and σ8

The existence of the three most massive clusters of galaxies observed so far at z>0. 5 is used to constrain the mass density parameter of the universe, Omega, and the amplitude of mass fluctuations, sigma₈. We find Omega=0. 2 (+0. 3, -0. 1), and sigma₈=1. 2 (+0. 5, -0. 4) (95 %). We show that the existence of even the single most distant cluster at z=0. 83, MS1054-03, with its large gravitational lensing mass, high temperature, and large velocity dispersion, is sufficient to establish powerful constraints. High-density, Omega=1 (sigma₈ ~ 0. 5-0. 6) Gaussian models are ruled out by these data (0. 65 (~10^-3 at z > 0. 5) instead of the 1 (3) clusters observed.