THE AMPLITUDE OF MASS FLUCTUATIONS IN THE UNIVERSE

We investigate how the rms linear fluctuation in the mass distribution on scales of 8 h-1 Mpc (denoted by sigma8) is constrained by the masses and abundances of rich clusters of galaxies. The derived value of sigma8 is almost independent of the shape of the fluctuation spectrum, but depends strongly on the cosmological density parameter. We find sigma8 almost-equal-to 0.52-0.62 for a critical density universe, and sigma8 almost-equal-to 1.25-1.58 for a spatially flat universe with OMEGA0 = 0.2. Our results conflict with the high amplitude inferred for an OMEGA = 1 cold dark matter universe from the COBE anisotropy measurements and advocated on other grounds by Couchman & Carlberg. However, our estimates of sigma8 are consistent with alternative models which provide a good fit to the observed shape of galaxy correlations on scales up to 50 h-1 Mpc and match on to the COBE results on larger scales.