Cosmic topology. Part IIIb. Eigenmodes and correlation matrices of spin-2 perturbations in orientable Euclidean manifolds

Abstract We study the eigenmodes of the spin-2 Laplacian in orientable Euclidean manifolds and their implications for the tensor-induced part of the cosmic microwave background (CMB) temperature and polarization anisotropies. We provide analytic expressions for the correlation matrices of Fourier-mode amplitudes and of spherical harmonic coefficients. We demonstrate that non-trivial spatial topology alters the statistical properties of CMB tensor anisotropies, inducing correlations between harmonic coefficients of differing ℓ and m and across every possible pair of temperature and E - and B -modes of polarization. This includes normally forbidden TB and EB correlations. We compute the Kullback-Leibler (KL) divergence between the pure tensor-induced CMB fluctuations in the usual infinite covering space and those in each of the non-trivial manifolds under consideration, varying both the size of the manifolds and the location of the observer. We find that the amount of information about the topology of the Universe contained in tensor-induced anisotropies does not saturate as fast as its scalar counterpart; indeed, the KL divergence continues to grow with the inclusion of higher multipoles up to the largest ℓ we have computed. Our results suggest that CMB polarization measurements from upcoming experiments can provide new avenues for detecting signatures of cosmic topology, motivating a full analysis where scalar and tensor perturbations are combined and noise is included.

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Publication Details

Journal
Journal of Cosmology and Astroparticle Physics
Published
2025-08-01
DOI
https://doi.org/10.1088/1475-7516/2025/08/015
Primary Topic
Cosmology and Gravitation Theories
Type
article
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article

Cosmic topology. Part IIIb. Eigenmodes and correlation matrices of spin-2 perturbations in orientable Euclidean manifolds

Anna Negro, Johannes R. Eskilt, Javier Carrón Duque, Craig J. Copi et al.
Journal of Cosmology and Astroparticle Physics
Cosmology and Gravitation Theories
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Cosmic topology. Part IIIb. Eigenmodes and correlation matrices of spin-2 perturbations in orientable Euclidean manifolds

Anna Negro, Johannes R. Eskilt, Javier Carrón Duque, Craig J. Copi, Deyan P. Mihaylov, Glenn D. Starkman, Andrew E. Jaffe, S Anselmi, Thiago S. Pereira, Arthur Kosowsky, Andrius Tamosiunas, Fernando Cornet-Gomez, Y. Akrami, Mikel Martin Barandiaran, Amirhossein Samandar, Joline Noltmann
article en

Abstract

Abstract We study the eigenmodes of the spin-2 Laplacian in orientable Euclidean manifolds and their implications for the tensor-induced part of the cosmic microwave background (CMB) temperature and polarization anisotropies. We provide analytic expressions for the correlation matrices of Fourier-mode amplitudes and of spherical harmonic coefficients. We demonstrate that non-trivial spatial topology alters the statistical properties of CMB tensor anisotropies, inducing correlations between harmonic coefficients of differing ℓ and m and across every possible pair of temperature and E - and B -modes of polarization. This includes normally forbidden TB and EB correlations. We compute the Kullback-Leibler (KL) divergence between the pure tensor-induced CMB fluctuations in the usual infinite covering space and those in each of the non-trivial manifolds under consideration, varying both the size of the manifolds and the location of the observer. We find that the amount of information about the topology of the Universe contained in tensor-induced anisotropies does not saturate as fast as its scalar counterpart; indeed, the KL divergence continues to grow with the inclusion of higher multipoles up to the largest ℓ we have computed. Our results suggest that CMB polarization measurements from upcoming experiments can provide new avenues for detecting signatures of cosmic topology, motivating a full analysis where scalar and tensor perturbations are combined and noise is included.

Journal of Cosmology and Astroparticle PhysicsVol. 2025(08)
Universidade Federal do Rio de Janeiro (BR), Universidade Estadual de Londrina (BR), Centre National de la Recherche Scientifique (FR), Consejo Superior de Investigaciones Científicas (ES), University of Padua (IT), University of Pittsburgh (US), University of Oslo (NO), Université Paris Cité (FR), Université Paris Sciences et Lettres (FR), Laboratoire Univers et Théories (FR), Istituto Nazionale di Fisica Nucleare, Sezione di Padova (IT), Instituto de Física Teórica (ES), Imperial College London (GB), University of Córdoba (ES), Case Western Reserve University (US), Universidad Autónoma de Madrid (ES), RWTH Aachen University (DE)
Openalex Percentile: Top 86%
Cosmology and Gravitation Theories
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