Propagating Cosmological Perturbations in a Bouncing Universe

TL;DR

This paper analyzes how cosmological perturbations evolve through a bouncing universe with positive spatial curvature and a scalar field, highlighting the scale dependence near NEC violation.

Contribution

It provides an explicit transition matrix for perturbations in a simple bouncing universe model, showing scale dependence near NEC violation.

Findings

Transition matrix depends on perturbation scale near NEC violation

Explicit relation between contracting and expanding phases

Highlights scale dependence in bouncing cosmology

Abstract

Using the simplest model for a bouncing universe, namely that for which gravity is described by pure general relativity, the spatial sections are positively curved and the matter content is a single scalar field, we obtain the transition matrix relating cosmological perturbation modes between the contracting and expanding phases. We show that this case provides a specific example in which this relation explicitely depends on the perturbation scale whenever the null energy condition (NEC) is close to be violated.