Constraining spatial curvature with large-scale structure

Abstract

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 $f{\sigma }_8$, 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 ${\Omega }_{\mathrm{m},0}=0.26\pm 0.04$ (68\% CL). When the clustering probes are combined with low-redshift background probes -- BAO and SNIa -- we obtain a CMB-independent constraint on curvature: ${\Omega }_{K,0}=0.0041{}_{-0.0504}^{+0.0500}$. We find no Bayesian evidence that the flat concordance model can be rejected. In addition we show that the sound horizon at decoupling is $r_{\mathrm{d}}=144.57\pm 2.34\mathrm{Mpc}$, in agreement with its measurement from CMB anisotropies. As a consequence, the late-time Universe is compatible with flat $\Lambda$CDM and a standard sound horizon, leading to a small value of $H_0$, {\em 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 ${\Omega }_{K,0}=-0.023\pm 0.010$.

40 pages; 13 figures; Version accepted by JCAP

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