The Structure of the Big Bang from Higher-Dimensional Embeddings

Details The Structure of the Big Bang from Higher-Dimensional Embeddings The Structure of the Big Bang from Higher-Dimensional Embeddings

2002-02-04

arxiv.org/abs/gr-qc/0202010v1

Class.Quant.Grav. 19 (2002) 1139-1155

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, 5 figures, revtex4, accepted in Class. Quant. Grav

Scientific paper

10.1088/0264-9381/19/6/307

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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