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Cosmological Constraints from the Large Scale Weak Lensing of SDSS MaxBCG Clusters

We derive constraints on the matter density \Om and the amplitude of matter clustering \sig8 from measurements of large scale weak lensing (projected separation R=5-30\hmpc) by clusters in the Sloan Digital Sky Survey MaxBCG catalog. The weak lensing signal is proportional to the product of \Om and the cluster-mass correlation function \xicm. With the relation between optical richness and cluster mass constrained by the observed cluster number counts, the predicted lensing signal increases with increasing \Om or \sig8, with mild additional dependence on the assumed scatter between richness and mass. The dependence of the signal on scale and richness partly breaks the degeneracies among these parameters. We incorporate external priors on the richness-mass scatter from comparisons to X-ray data and on the shape of the matter power spectrum from galaxy clustering, and we test our adopted model for \xicm against N-body simulations. Using a Bayesian approach with minimal restrictive priors, we find \sig8(\Om/0.325)^{0.501}=0.828 +/- 0.049, with marginalized constraints of \Om=0.325_{-0.067}^{+0.086} and \sig8=0.828_{-0.097}^{+0.111}, consistent with constraints from other MaxBCG studies that use weak lensing measurements on small scales (R<=2\hmpc). The (\Om,\sig8) constraint is consistent with and orthogonal to the one inferred from WMAP CMB data, reflecting agreement with the structure growth predicted by GR for an LCDM cosmological model. A joint constraint assuming LCDM yields \Om=0.298 +/- 0.020 and \sig8=0.831 +/- 0.020. Our cosmological parameter errors are dominated by the statistical uncertainties of the large scale weak lensing measurements, which should shrink sharply with current and future imaging surveys.