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We investigate how the rms linear fluctuation in the mass distribution on scales of 8 h–1 Mpc1 (denoted by σ8) is constrained by the masses and abundances of rich clusters of galaxies. The derived value of σ8 is almost independent of the shape of the fluctuation spectrum, but depends strongly on the cosmological density parameter. We find σ8 ≈ 0.52–0.62 for a critical density universe, and σ8 ≈ 1.25–1.58 for a spatially flat universe with Ω = 0.2. Our results conflict with the high amplitude inferred for an Ω = 1 cold dark matter universe from the COBE anisotropy measurements and advocated on other grounds by Couchman & Carlberg. However, our estimates of σ8 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.
White et al. (1993) studied this question.