FLRW embeddings in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="double-struck">R</mi><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msup></math>, differential geometry and conformal photon propagator

E. Huguet; J. Queva; J. Renaud

doi:10.1103/x3g4-b6s9

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

E. Huguet ^1,*, J. Queva ^2,†, and J. Renaud ^3,‡

¹Université Paris Cité, APC-Astroparticule et Cosmologie (CNRS UMR 7164), Batiment Condorcet, 10 rue Alice Domon et Léonie Duquet, F-75205 Paris Cedex 13, France
²Université de Corse—CNRS, UMR 6134 SPE, Campus Grimaldi BP 52, 20250 Corte, France
³APC-Astroparticule et Cosmologie (CNRS UMR 7164), Batiment Condorcet, 10 rue Alice Domon et Léonie Duquet, F-75205 Paris Cedex 13, France

^*Contact author: huguet@apc.univ-paris7.fr
^†Contact author: queva@univ-corse.fr
^‡Contact author: jrenaud@apc.in2p3.fr

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Phys. Rev. D 113, 065018 – Published 24 March, 2026

DOI: https://doi.org/10.1103/x3g4-b6s9

Abstract

This paper introduces differential-geometric methods to study $n$ -dimensional locally conformally flat spaces as submanifolds in $R^{n + 2}$ . 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.

Physical Review D

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

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FLRW embeddings in Rn+2, differential geometry and conformal photon propagator

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