  We determine the linear amplitude of mass fluctuations in the universe,
sigma_8, from the abundance of massive clusters at redshifts z=0.5 to 0.8. The
evolution of massive clusters depends exponentially on the amplitude of mass
fluctuations and thus provides a powerful measure of this important
cosmological parameter. The relatively high abundance of massive clusters
observed at z>0.5, and the relatively slow evolution of their abundance with
time, suggest a high amplitude of mass fluctuations: sigma_8=0.9 +-10% for
Omega_m=0.4, increasing slightly to sigma_8=0.95 for Omega_m=0.25 and
sigma_8=1.0 for Omega_m=0.1 (flat CDM models). We use the cluster abundance
observed at z=0.5 to 0.8 to derive a normalization relation from the
high-redshift clusters, which is only weakly dependent on Omega_m:
sigma_8*Omega_m^0.14 = 0.78 +-0.08. When combined with recent constraints from
the present-day cluster mass function (sigma_8*Omega_m^0.6=0.33 +-0.03) we find
sigma_8=0.98 +-0.1 and Omega_m=0.17 +-0.05. Low sigma_8 values (<0.7) are
unlikely; they produce an order of magnitude fewer massive clusters than
observed.
