A Note on Perturbations During a Regular Bounce

TL;DR

This paper critiques a common method for analyzing scalar perturbations in bouncing cosmologies, identifies its inconsistency with energy-momentum conservation, and proposes a new, well-behaved solution approach.

Contribution

It highlights a flaw in existing perturbation methods and introduces a novel, consistent technique for studying scalar perturbations in regular bouncing universes.

Findings

Identifies inconsistency in a widely used perturbation method.

Proposes a new method with two independent, well-behaved solutions.

Ensures solutions are consistent with energy-momentum conservation.

Abstract

We point out an inconsistency in a method used in the literature for studying adiabatic scalar perturbations in a regular bouncing universe (in four dimensions). The method under scrutiny consists of splitting the Bardeen potential into two pieces with independent evolutions, in order to avoid a singular behavior at the boundaries of the region where the null energy condition (NEC) is violated. However, we argue that this method violates energy-momentum conservation. We then introduce a novel method which provides two independent solutions for the Bardeen potential around the boundaries, even in the case of adiabatic perturbations. The two solutions are well behaved and not divergent.