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,
Omega, and the amplitude of mass fluctuations, sigma_8. We find Omega=0.2
(+0.3,-0.1), and sigma_8=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 (sigma_8 ~
0.5-0.6) Gaussian models are ruled out by these data (< 10^-6 probability);
the Omega=1 models predict only ~10^-5 massive clusters at z > 0.65 (~10^-3
at z > 0.5) instead of the 1 (3) clusters observed.
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