{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/constraining-spatial-curvature-with-large","title":"Constraining spatial curvature with large-scale structure","arxiv_id":"2206.03059","date":"2022-06-07","proceeding":null,"authors":["Julien Bel","Julien Larena","Roy Maartens","Christian Marinoni","Louis Perenon"],"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 $\\Omega_{{\\rm m}, 0}=0.26\\pm 0.04$ (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 $r_{\\rm d} = 144.57 \\pm 2.34 \\; {\\rm Mpc}$, 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 $\\Omega_{K,0}= -0.023 \\pm 0.010$.","url_abs":"https://arxiv.org/abs/2206.03059v4","url_pdf":"https://arxiv.org/pdf/2206.03059v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"constraining-spatial-curvature-with-large","repo_url":"https://github.com/louisperenon/eclair_likelihoods","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}