Time-Dependent Warping and Non-Singular Bouncing Cosmologies

TL;DR

This paper constructs six-dimensional, non-singular, time-dependent warped cosmological solutions that bounce periodically without violating energy conditions, and explores topology-changing singular solutions.

Contribution

It introduces a new class of non-singular, time-dependent warped solutions in six-dimensional gravity supporting bouncing cosmologies.

Findings

Non-singular solutions with periodic bounces

Support by matter satisfying null energy condition

Existence of topology-changing singular solutions

Abstract

In this note, we construct a family of non-singular time-dependent solutions of a six-dimensional gravitational theory that are warped products of a four dimensional bouncing cosmological solution and a two dimensional internal manifold. The warp factor is time-dependent and breaks translation invariance along one of the internal directions. When the warp factor is periodic in time, the non-compact part of the geometry bounces periodically. The six dimensional geometry is supported by matter that does not violate the null energy condition. We show that this 6D geometry does not admit a closed trapped surface and hence the Hawking-Penrose singularity theorems do not apply to these solutions. We also present examples of singular solutions where the topology of the internal manifold changes dynamically.