Five-dimensional null-cone structure of big bang singularity

Abstract

Firedmann model Φ of positive space curvature, vanishing pressure and cosmological constant when isometrically imbedded as a hypersurface in five dimensional Minkowski spaceM ⁵ is globally rigid: if F(Φ) and F′(Φ) are isometric imbeddings inM ⁵ there is a motion π of M⁵ such that F= π°f. The big bang singularity is the vertex of a null half-cone inM ⁵. Global rigidity leads to an invariant characterization of the singularity. The structure of matter at the singularity is governed by the de Sitter group.