A Simple Harmonic Universe

TL;DR

This paper presents stable, non-singular bouncing solutions in general relativity supported by specific matter and curvature conditions, with potential implications for cosmological models.

Contribution

It introduces a class of simple, stable bouncing solutions in general relativity that avoid singularities and can oscillate multiple times, expanding the landscape of cosmological models.

Findings

Solutions are classically stable for moderate bounces.

Solutions can oscillate many times before instabilities occur.

Quantum effects eventually lead to a singular crunch.

Abstract

We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k=+1, and are supported by a negative cosmological term and matter with -1 < w < -1/3. In the case of moderate bounces (where the ratio of the maximal scale factor $a_+$ to the minimal scale factor $a_-$ is ${\cal O}(1)$), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large $a_+/a_-$, the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.