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
[49].
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
[50].
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
[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].