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

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 amplit...

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Detalles Bibliográficos
Autores: Samandar, A., Duque, J.C., Copi, C.J., Barandiaran, M.M., Mihaylov, D.P., Starkman, G.D., Akrami, Y., Anselmi, S., Cornet-Gomez, F., Eskilt, J.R., Jaffe, A.H., Kosowsky, A., Negro, A., Noltmann, J., Pereira, T.S., Tamosiunas, A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:dnet:digitalcsic_::d21f9226ead41272c1a0fb5ac9cb842b
Acceso en línea:http://hdl.handle.net/10261/427300
https://www.scopus.com/inward/record.uri?eid=2-s2.0-105012559148&doi=10.1088%2F1475-7516%2F2025%2F08%2F015&partnerID=40&md5=766e04ee319964d8f02fe6939a5f266d
Access Level:acceso abierto
Palabra clave:CMBR polarisation
CMBR theory
cosmological perturbation theory
cosmology of theories beyond the SM
Descripción
Sumario: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. © 2025 The Author(s)

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