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

Abstract

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.

v1: 37 pages, 4 figures, v2: typos corrected, v3: close match to published article