Cosmological constraints from galaxy clustering and the mass-to-number ratio of galaxy clusters

We place constraints on the average density (Ω_m) and clustering amplitude (σ₈) of matter using a combination of two measurements from the Sloan Digital Sky Survey: the galaxy two-point correlation function, w_p (r_p), and the mass-to-galaxy-number ratio within galaxy clusters, M/N, analogous to cluster M/L ratios. Our w_p (r_p) measurements are obtained from DR7 while the sample of clusters is the maxBCG sample, with cluster masses derived from weak gravitational lensing. We construct nonlinear galaxy bias models using the Halo Occupation Distribution (HOD) to fit both w_p (r_p) and M/N for different cosmological parameters. HOD models that match the same two-point clustering predict different numbers of galaxies in massive halos when Ω_m or σ₈ is varied, thereby breaking the degeneracy between cosmology and bias. We demonstrate that this technique yields constraints that are consistent and competitive with current results from cluster abundance studies, without the use of abundance information. Using w_p (r_p) and M/N alone, we find Ω^0.5 _mσ₈ = 0.465 0.026, with individual constraints of Ω_m = 0.29 0.03 and σ₈ = 0.85 0.06. Combined with current cosmic microwave background data, these constraints are Ω_m = 0.290 0.016 and σ₈ = 0.826 0.020. All errors are 1σ. The systematic uncertainties that the M/N technique are most sensitive to are the amplitude of the bias function of dark matter halos and the possibility of redshift evolution between the SDSS Main sample and the maxBCG cluster sample. Our derived constraints are insensitive to the current level of uncertainties in the halo mass function and in the mass-richness relation of clusters and its scatter, making the M/N technique complementary to cluster abundances as a method for constraining cosmology with future galaxy surveys.