Mass Function of Rich Galaxy Clusters and Its Constraint on sigma_8
  The mass function of galaxy clusters is a powerful tool to constrain
cosmological parameters, e.g., the mass fluctuation on the scale of 8 h^{-1}
Mpc, sigma_8, and the abundance of total matter, Omega_m. We first determine
the scaling relations between cluster mass and cluster richness, summed r-band
luminosity and the global galaxy number within a cluster radius. These
relations are then used to two complete volume-limited rich cluster samples
which we obtained from the Sloan Digital Sky Survey (SDSS). We estimate the
masses of these clusters and determine the cluster mass function. Fitting the
data with a theoretical expression, we get the cosmological parameter
constraints in the form of sigma_8(Omega_m/0.3)^{alpha}=beta and find out the
parameters of alpha=0.40-0.50 and beta=0.8-0.9, so that sigma_8=0.8-0.9 if
Omega_m=0.3. Our sigma_8 value is slightly higher than recent estimates from
the mass function of X-ray clusters and the Wilkinson Microwave Anisotropy
Probe (WMAP) data, but consistent with the weak lensing statistics.
