Cosmologies with turning points

Abstract

We explore singularity-free and geodesically-complete cosmologies based on manifolds that are not quite Lorentzian. The metric can be either smooth everywhere or non-degenerate everywhere, but not both, depending on the coordinate system. The smooth metric gives an Einstein tensor that is first order in derivatives while the non-degenerate metric has a piecewise FLRW form. On such a manifold the universe can transition from expanding to contracting, or vice versa, with the Einstein equations satisfied everywhere and without violation of standard energy conditions. We also obtain a corresponding extension of the Kasner vacuum solutions on such manifolds.

12 pages, to appear in Physics Letters B

Cited by in corpus (3)

• Complex degenerate metrics in general relativity: a covariant extension of the Moore-Penrose algorithm
• Nonsingular solutions to the Einstein equations on piecewise-Lorentzian manifolds
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations