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FLRW embeddings in $\mathbb{R}^{n+2}$, differential geometry and conformal photon propagator

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  • Additional Information
    • Contributors:
      AstroParticule et Cosmologie (APC (UMR_7164)); Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris; Centre National de la Recherche Scientifique (CNRS)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité); Laboratoire « Sciences pour l’Environnement » (UMR CNRS 6134 SPE) (SPE); Centre National de la Recherche Scientifique (CNRS)-Università di Corsica Pasquale Paoli Université de Corse Pascal Paoli
    • Publication Information:
      CCSD
    • Publication Date:
      2026
    • Abstract:
      International audience ; This paper introduces differential-geometric methods to study $n$-dimensional locally conformally flat spaces as submanifolds in $\mathbb{R}^{n+2}$. We derive explicit formulas relating intrinsic and ambient differential-geometric objects, including curvature tensors, the codifferential and laplacian operators. We apply this approach to Friedmann-Lemaître-Robertson-Walker (FLRW) spaces using newfound embedding formulas, obtaining new and simplified expressions for the photon propagator in four dimensions.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2512.10901; ARXIV: 2512.10901; INSPIRE: 3092174
    • Accession Number:
      10.1103/x3g4-b6s9
    • Online Access:
      https://hal.science/hal-05429938
      https://hal.science/hal-05429938v1/document
      https://hal.science/hal-05429938v1/file/2512.10901v3.pdf
      https://doi.org/10.1103/x3g4-b6s9
    • Rights:
      https://creativecommons.org/licenses/by-nc-sa/4.0/ ; info:eu-repo/semantics/OpenAccess
    • Accession Number:
      edsbas.93A533E0