Cosmological constraints from the large-scale weak lensing of SDSS MaxBCG clusters

We derive constraints on the matter density Ω_m and the amplitude of matter clustering σ₈ from measurements of large-scale weak lensing (projected separation R = 5-30 h^-1 Mpc) by clusters in the Sloan Digital Sky Survey MaxBCG catalogue. The weak lensing signal is proportional to the product of Ω_m and the cluster-mass correlation function ξ_cm. With the relation between optical richness and cluster mass constrained by the observed cluster number counts, the predicted lensing signal increases with increasing Ω_m or σ₈, 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 ξ_cm against N-body simulations. Using a Bayesian approach with minimal restrictive priors, we find σ₈(Ω_m/0.325)^0.501 = 0.828 ± 0.049, with marginalized constraints of Ω _m=0.325_{-0.067}^{+0.086} and σ _8=0.828_{-0.097}^{+0.111}, consistent with constraints from other MaxBCG studies that use weak lensing measurements on small scales (R ≤ 2 h^-1 Mpc). The (Ω_m, σ₈) constraint is consistent with and orthogonal to the one inferred from Wilkinson Microwave Anisotropy Probe cosmic microwave background data, reflecting agreement with the structure growth predicted by General Relativity for a Λ cold dark matter (ΛCDM) cosmological model. A joint constraint assuming ΛCDM yields Ω _m=0.298_{-0.020}^{+0.019} and σ _8=0.831_{-0.020}^{+0.020}. For these parameters and our best-fitting scatter, we obtain a tightly constrained mean richness-mass relation of MaxBCG clusters, N₂₀₀ = 25.4(M/3.61 × 10¹⁴ h^-1 M_⊙)^0.74, with a normalization uncertainty of 1.5 per cent. 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.