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4.4. Cluster Abundance and Correlations

If clusters can be modeled (e.g., using an improved version of the Press-Schechter formalism) as ``objects'' above a mass threshold in a density fluctuation field that was initially Gaussian, then the cluster mass function can be used to constrain sigma8 Omegam0.6 [49]. The correlation amplitude of these clusters can be compared with their abundance to give a direct measure of sigma8. Together, these results yield Omegam and sigma8 separately [50].

Pro: The two parameters are determined from observational data that are relatively easy to obtain. bullet The method depends sensitively only on the assumptions of Gaussian statistics and of mass-limited cluster definition. It is insensitive to the actual power spectrum of fluctuations.

Con: The amplitude of cluster correlations still carries a large uncertainty. bullet The method relies on the assumption of Gaussian initial conditions.

Current Results: sigma8 Omegam0.6 appeq 0.5 - 0.6 [49] from cluster abundances (compare to Section 4.1), but measures of the cluster autocorrelation strength are still too uncertain to be able to give a useful second constraint [50].