Constraining spatial curvature with large-scale structure

We analyse the clustering of matter on large scales in an extension of the con-cordance 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 f sigma 8, which differs significantly from empirical models in the literature. A key innovation is the use of the `Clustering Ra-tio', 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 S2m,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: QK,0 = 0.0041 +0.0500 -0.0504. We find no Bayesian evidence that the flat concor-dance model can be rejected. In addition we show that the sound horizon at decoupling is rd = 144.57 +/- 2.34 Mpc, in agreement with its measurement from CMB anisotropies. As a consequence, the late-time Universe is compatible with flat ACDM and a standard sound horizon, leading to a small value of H0, without assuming any CMB information. Clustering Ratio measurements produce the only low-redshift clustering data set that is not in disagree-ment with the CMB, and combining the two data sets we obtain QK,0 = -0.023 +/- 0.010.

Automated summary

This study analyzes the clustering of matter on large scales considering spatial curvature and develops a consistent approach to calculate the 2-point correlation function in redshift space. The use of the 'Clustering Ratio' as a probe of clustering, in combination with low-redshift background probes, provides powerful cosmological constraints independent of CMB information. The study finds that the flat concordance model with curvature is consistent with the observed data, and the use of clustering ratio measurements can provide valuable low-redshift clustering data that is compatible with the CMB.