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The Structure of the Big Bang from Higher-Dimensional Embeddings

Sanjeev S. Seahra·Paul S. Wesson
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Abstract

We give relations for the embedding of spatially-flat Friedmann-Robertson-Walker cosmological models of Einstein's theory in flat manifolds of the type used in Kaluza-Klein theory. We present embedding diagrams that depict different 4D universes as hypersurfaces in a higher dimensional flat manifold. The morphology of the hypersurfaces is found to depend on the equation of state of the matter. The hypersurfaces possess a line-like curvature singularity infinitesimally close to the $t = 0^+$ 3-surface, where $t$ is the time expired since the big bang. The family of timelike comoving geodesics on any given hypersurface is found to have a caustic on the singular line, which we conclude is the 5D position of the point-like big bang.

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Sanjeev S. Seahra, Paul S. Wesson. 2002-02-04. The Structure of the Big Bang from Higher-Dimensional Embeddings. https://doi.org/10.1088/0264-9381%2F19%2F6%2F307

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