Year: 2026
Type: preprint
Abstract: The global topology of the Universe is a longstanding open question. In this work, we examine the statistical signatures of a positively curved universe with a Friedmann--Lemaitre--Robertson--Walker metric and the topology of a lens space $L(p,q)$. Since these manifolds are generally statistically anisotropic and inhomogeneous, their cosmic microwave background (CMB) covariance matrices contain non-zero off-diagonal entries that depend on observer location. We compute these full harmonic-space covariance matrices for scalar perturbations for arbitrary lens spaces and observer position. Using the Kullback--Leibler divergence, we assess the distinguishability of these spaces from a simply connected three-sphere with the same curvature. The results show that topological signatures can still be significant in a cosmic-variance-limited regime even when the length, $d_{\rm NC}$, of the shortest loop around the Universe through the observer exceeds the diameter, $d_{\rm LSS}$, of the last-scattering surface by up to $10\%$. This distinguishability depends on the curvature, the lens space and the observer position mainly through the ratio $d_{\rm NC}/d_{\rm LSS}$, which is set not only by the curvature radius but also by $p$, $q$ and the observer location. Therefore, for any value of the spatial curvature, however small, there are lens spaces and observer positions for which $0.985\,d_{\rm LSS}
Source: arXiv (Cornell University)
Authors: Barandiaran, Mikel Martin, Petretti, Catherine, Anselmi, Stefano, Mihaylov, Deyan P., Negro, Anna, Starkman, Glenn D., Tamosiunas, Andrius, Akrami, Yashar, Alestas, George, Duque, Javier Carrón, Copi, Craig J., Cornet-Gomez, Fernando, Lu, Linn Htat, Jaffe, Andrew H., Kosowsky, Arthur, Gómez, José Javier Ortega, Rodrigues, Ricardo G., Samandar, Amirhossein, Trendafilova, Cynthia
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: U.S. Department of Energy, National Aeronautics and Space Administration, Harvard University, Case Western Reserve University, Ministerio de Ciencia, Innovación y Universidades, European Commission, Bulgarian National Science Fund, Faculty of Arts and Sciences, HORIZON EUROPE Framework Programme, Science and Technology Facilities Council, Consejo Superior de Investigaciones Científicas, Agencia Estatal de Investigación, Spanish National Plan for Scientific and Technical Research and Innovation, European Social Fund, NextGenerationEU
Awards: G1105844351, G1349947283, G1513814287, G1746333638, G179674260, G1799927510, G2311573283, G2333236004, G2551911579, G282847690, G318412399, G3452655474, G4115556258, G4273564781, THEORETICAL PARTICLE PHYSICS AT THE FRONTIERS, G491712853, G4993905653, G5180915604, G5195188938, G5404395142, G546199279, G5635532810, G5662822759, G5865811434, G58976015, G5939349724, G6080697404, G6218905885, G624877701, G6326031618, G6520718613, G7351490666, G7805626310, G7863371703, G8118709007, G8497050386, G855041801, G8793339930, G8888022036
OpenAlex ID: W7221159679