### Abstract

We derive constraints on the matter density ω_{m} and the amplitude of matter clustering σ_{8} 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 σ_{8}, 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 σ_{8}(ω_{m}/0.325)^{0.501} = 0.828 ± 0.049, with marginalized constraints of ω_{m} = 0.325^{+0.086} _{-0.067} and σ_{8} = 0.828^{+0.111} _{-0.097}, consistent with constraints from other MaxBCG studies that use weak lensing measurements on small scales (R ≤ 2 h^{-1} Mpc). The (ω_{m}, σ_{8}) 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 δ cold dark matter (δCDM) cosmological model. A joint constraint assuming δCDMyieldsω_{m} = 0.298^{+0.019} _{-0.020} 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, N_{200} = 25.4(M/3.61 × 10^{14}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.

Original language | English (US) |
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Pages (from-to) | 1628-1647 |

Number of pages | 20 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 439 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2014 |

Externally published | Yes |

### Keywords

- Cosmological parameters
- Large-scale structure of Universe
- Methods: statistical

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Monthly Notices of the Royal Astronomical Society*,

*439*(2), 1628-1647. https://doi.org/10.1093/mnras/stu033