Abstract
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, Ω, and the amplitude of mass fluctuations, σ8. We find Ω=0.2−0.1+0.3 and σ8=1.2−0.4+0.5 (95%). We show that the existence of even the single most distant cluster at z = 0.83, MS 1054-03, with its large gravitational lensing mass, high temperature, and large velocity dispersion, is sufficient to establish powerful constraints. High-density, Ω = 1 (σ8 ≃ 0.5-0.6) Gaussian models are ruled out by these data (≲10-6 probability); the Ω = 1 models predict only ~10-5 massive clusters at z > 0.65 (~10-3 at z > 0.5) instead of the one (three) clusters observed.
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