General solution for scalar perturbations in bouncing cosmologies

TL;DR

This paper analyzes how scalar perturbations evolve through a cosmological bounce in flat universes, identifying conditions under which the primordial spectrum remains scale-invariant, thus supporting bouncing cosmologies as an alternative to inflation.

Contribution

It provides a general framework for evolving scalar perturbations in flat bouncing cosmologies, highlighting the importance of the pressure perturbation relation for spectrum preservation.

Findings

The pre-bounce scale-invariant spectrum can survive the bounce under specific conditions.

Bouncing models with extra dimensions are included in the analysis.

Bounces with positive spatial curvature require a different treatment.

Abstract

Bouncing cosmologies, suggested by String/M-theory, may provide an alternative to standard inflation to account for the origin of inhomogeneities in our universe. The fundamental question regards the correct way to evolve the scalar perturbations through the bounce. In this work, we determine the evolution of perturbations and the final spectrum for an arbitrary (spatially flat) bouncing cosmology, with the only assumption that the bounce is governed by a single physical scale. In particular, we find that the spectrum of the pre-bounce growing mode of the Bardeen potential (which is scale-invariant in some limit, and thus compatible with observations) survives unaltered in the post-bounce only if the comoving pressure perturbation is directly proportional to the Bardeen potential rather than its Laplacian, as for any known form of ordinary matter. If some new physics acting at the bounce justifies such relation, then bouncing cosmologies are entitled to become a real viable alternative for the generation of the observed inhomogeneities. Our treatment also includes some class of models with extra-dimensions, whereas we show that bounces induced by positive spatial curvature are structurally different from all bounces in spatially flat universes, requiring a distinct analysis.