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We derive constraints on the matter density \Om and the amplitude of matterclustering \sig8 from measurements of large scale weak lensing (projectedseparation R=5-30\hmpc) by clusters in the Sloan Digital Sky Survey MaxBCGcatalog. The weak lensing signal is proportional to the product of \Om and thecluster-mass correlation function \xicm. With the relation between opticalrichness and cluster mass constrained by the observed cluster number counts,the predicted lensing signal increases with increasing \Om or \sig8, with mildadditional dependence on the assumed scatter between richness and mass. Thedependence of the signal on scale and richness partly breaks the degeneraciesamong these parameters. We incorporate external priors on the richness-massscatter from comparisons to X-ray data and on the shape of the matter powerspectrum from galaxy clustering, and we test our adopted model for \xicmagainst N-body simulations. Using a Bayesian approach with minimal restrictivepriors, we find \sig8(\Om/0.325)^{0.501}=0.828 +/- 0.049, with marginalizedconstraints 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 lensingmeasurements on small scales (R<=2\hmpc). The (\Om,\sig8) constraint isconsistent with and orthogonal to the one inferred from WMAP CMB data,reflecting agreement with the structure growth predicted by GR for an LCDMcosmological model. A joint constraint assuming LCDM yields \Om=0.298 +/- 0.020and \sig8=0.831 +/- 0.020. Our cosmological parameter errors are dominated bythe statistical uncertainties of the large scale weak lensing measurements,which should shrink sharply with current and future imaging surveys.

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