Generalised perturbation equations in bouncing cosmologies

TL;DR

This paper derives general perturbation equations for bouncing cosmologies in modified gravity, showing how long-wavelength scalar perturbations evolve through a bounce and analyzing their spectrum transfer in ekpyrotic models.

Contribution

It provides a unified framework for linear perturbations in non-singular bouncing cosmologies within generalized gravity theories.

Findings

Perturbation equations reduce to familiar forms in GR with no anisotropic stress.

Scale-invariant spectra in collapse phases are not transferred to the expanding phase.

Homogeneous second-order differential equations describe large-scale perturbations in a pseudo-longitudinal gauge.

Abstract

We consider linear perturbation equations for long-wavelength scalar metric perturbations in generalised gravity, applicable to non-singular cosmological models including a bounce from collapse to expansion in the very early universe. We present the general form for the perturbation equations which follows from requiring that the inhomogeneous universe on large scales obeys the same local equations as the homogeneous Friedmann-Robertson-Walker background cosmology (the separate universes approach). In a pseudo-longitudinal gauge this becomes a homogeneous second-order differential equation for adiabatic perturbations, which reduces to the usual equation for the longitudinal gauge metric perturbation in general relativity with vanishing anisotropic stress. As an application we show that the scale-invariant spectrum of perturbations in the longitudinal gauge generated during an ekpyrotic collapse are not transferred to the growing mode of adiabatic density perturbations in the expanding phase in a simple bounce model.