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 8 m0.6 . The correlation amplitude of these clusters can be compared with their abundance to give a direct measure of 8. Together, these results yield m and 8 separately .
Pro: The two parameters are determined from observational data that are relatively easy to obtain. 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. The method relies on the assumption of Gaussian initial conditions.
Current Results: 8 m0.6 0.5 - 0.6  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 .