The Friedmann-Lemaitre models in perspective

Abstract

I show that all FRW models (four dimensional pseudo-Riemannian manifolds with maximally symmetric space) can be embedded in a flat Minkowski manifold with 5 dimensions. The pseudo Riemannian metric of space-time is induced by the flat metric. This generalizes the usual embedding widely used for the \dS ~models. I give the coordinate transformations for the embedding. Taking into account the spatial isotropy, one can reduce space-time to a two-dimensional surface, embedded in a three-dimensional Minkowski space. This allows to give exact graphic representations of the FRW models, and in particular of their curvature.

Embeddings of Friedmann-Lemaitre models in flat 5-dimensional space 7 pages, 7 figures, article