Abstract
We derive constraints on the matter density Ωm 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 Ωm and the cluster-mass correlation function ξcm. With the relation between optical richness and cluster mass constrained by the observed cluster number counts, the predicted lensing signal increases with increasing Ωm 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 ξcm against N-body simulations. Using a Bayesian approach with minimal restrictive priors, we find σ8(Ωm/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 (Ωm, 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.
Author
Zu, Ying; Weinberg, David H.; Rozo, Eduardo; Sheldon, Erin S.; Tinker, Jeremy L.; Becker, Matthew R.
Journal
Monthly Notices of the Royal Astronomical Society
Paper Publication Date
February 2014
Paper Type
Astrostatistics