Large Adiabatic Scalar Perturbations in a Regular Bouncing Universe

TL;DR

This paper investigates the behavior of scalar perturbations in a bouncing universe, showing that the amplitude of growing modes can become large, and discusses gauge choices and conditions for valid linear perturbation theory.

Contribution

It demonstrates that large adiabatic scalar perturbations are a general feature in regular bouncing cosmologies and identifies gauge conditions ensuring the validity of linear perturbation analysis.

Findings

Growing mode amplitudes can exceed unity near the bounce.

A gauge exists where perturbation theory remains valid throughout the bounce.

Certain gauge-fixing conditions may be ill-defined for some solutions.

Abstract

It has been shown that a contracting universe with a dust-like ($w \approx 0$) fluid may provide an almost scale invariant spectrum for the gravitational scalar perturbations. As the universe contracts, the amplitude of such perturbations are amplified. The gauge invariant variable $\Phi$ develops a growing mode which becomes much larger than the constant one around the bounce phase. The constant mode has its amplitude fixed by Cosmic Background Explorer (COBE) normalization, thus the amplitude of the growing mode can become much larger than 1. In this paper, we first show that this is a general feature of bouncing models, since we expect that general relativity should be valid in all scales away from the bounce. However, in the Newtonian gauge, the variable $\Phi$ gives the value of the metric perturbation $\phi$, raising doubts on the validity of the linear perturbative regime at the bounce. In order to address this issue, we obtain a set of necessary conditions for the perturbative series to be valid along the whole history of the model, and we show that there is a gauge in which all these conditions are satisfied, for a set of models, if the constant mode is fixed by COBE normalization. As a by-product of this analysis, we point out that there are sets of solutions for the perturbation variables where some gauge-fixing conditions are not well defined, turning these gauges prohibited for those solutions.