Cosmologies with turning points

TL;DR

This paper investigates singularity-free, geodesically-complete cosmological models on manifolds with non-standard Lorentzian structures, allowing universe transitions between expansion and contraction without violating energy conditions.

Contribution

It introduces novel cosmological solutions on manifolds that are not strictly Lorentzian, enabling universe turning points without singularities or energy condition violations.

Findings

Existence of smooth and non-degenerate metric solutions with universe turning points.

Extension of Kasner vacuum solutions to these non-standard manifolds.

Models are singularity-free and satisfy Einstein equations everywhere.

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.