The amplitude of mass fluctuations in the Universe

Abstract

We investigate how the rms linear fluctuation in the mass distribution on scales of 8/h Mpc (denoted by sigma(8)) is constrained by the masses and abundances of rich clusters of galaxies. The derived value of sigma(8) is almost independent of the shape of the fluctuation spectrum, but depends strongly on the cosmological density parameter. We find sigma(8) of about 0.52-0.62 for a critical density universe, and sigma(8) of about 1.25-1.58 for a spatially flat universe with Omega(0) = 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 (1992). However, our estimates of sigma(8) are consistent with alternative models which provide a good fit to the observed shape of galaxy correlations on scales up to 50/h Mpc and match on to the COBE results on larger scales.