| Abstract
| - We show that it may be possible to determine both the cosmic density parameter Ω0 and the amplitude of cosmic mass fluctuations σ8 by using large redshift surveys of galaxies and galaxy clusters. If a cluster sample can be considered complete above some mass threshold, then hierarchical theories for structure formation predict its autocorrelation function to be determined purely by the cluster abundance and by the spectrum of linear density fluctuations. Thus, if the shape of the initial fluctuation spectrum is known, its amplitude σ8 can be estimated directly from the correlation length of a cluster sample in a way that is independent of the value of Ω0. If the cluster mass corresponding to the sample threshold is also known, it provides an independent estimate of the quantity σ8Ω00.6. Thus cluster data should allow both σ8 and Ω0 to be determined observationally. We explore this possibility using N-body simulations together with a simple but accurate analytical model based on extensions of Press-Schechter theory. Applying our results to currently available data, we find that if the linear fluctuation spectrum has a shape similar to that suggested by the APM galaxy survey, then a correlation length r0 in excess of 20 h−1 Mpc for Abell clusters would require σ8 ≲ l, while r0< 15 h−1 Mpc would require σ8 ≲ 0.5. With conventional estimates of the relevant mass threshold, these imply Ω0 ≲ 0.3 and Ω0 ≳1 respectively.
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