Unstable growth of curvature perturbation in non-singular bouncing cosmologies

TL;DR

This paper analyzes the evolution of curvature perturbations in non-singular bouncing cosmologies, revealing an instability that can disrupt the scale-invariant spectrum, and discusses potential solutions.

Contribution

It demonstrates that adiabatic curvature perturbations are exponentially amplified near the bounce in non-singular models, challenging their viability.

Findings

Perturbations grow exponentially before the bounce when w approaches -1.

The scale-invariant spectrum can be spoiled by this growth.

Singular bounces may avoid this instability.

Abstract

We consider non-singular bouncing cosmologies, such as the new ekpyrotic model, in which the universe undergoes a slow contraction phase with equation of state $w \gg 1$, followed by a bounce that occurs at a finite scale factor when quantum gravity corrections are still negligible. Such a non-singular bounce requires a violation of the null energy condition in which $w$ falls below -1 at some time before the bounce. In this paper, we show that a component of the adiabatic curvature perturbations, though decaying and negligible during the ekpyrotic phase, is exponentially amplified just before $w$ approaches -1, enough to spoil the scale-invariant perturbation spectrum. We discuss how the problem may be avoided, for example, in singular bounces.