Constraining spatial curvature with large-scale structure

We analyse the clustering of matter on large scales in an extension of the concordance model that allows for spatial curvature. We develop a consistent approach to curvature and wide-angle effects on the galaxy 2-point correlation function in redshift space. In particular we derive the Alcock-Paczynski distortion of fσ 8, which differs significantly from empirical models in the literature. A key innovation is the use of the 'Clustering Ratio', which probes clustering in a different way to redshift-space distortions, so that their combination delivers more powerful cosmological constraints. We use this combination to constrain cosmological parameters, without CMB information. In a curved Universe, we find that ωm, 0=0.26± 0.04 (68% CL). When the clustering probes are combined with low-redshift background probes - BAO and SNIa - we obtain a CMB-independent constraint on curvature: ωK, 0 = 0.0041-0.0504+0.0500. We find no Bayesian evidence that the flat concordance model can be rejected. In addition we show that the sound horizon at decoupling is r d = 144.57 ± 2.34 Mpc, in agreement with its measurement from CMB anisotropies. As a consequence, the late-time Universe is compatible with flat ΛCDM and a standard sound horizon, leading to a small value of H 0, without assuming any CMB information. Clustering Ratio measurements produce the only low-redshift clustering data set that is not in disagreement with the CMB, and combining the two data sets we obtain ωK, 0 = -0.023 ± 0.010.