Growth of covariant perturbations in the contracting phase of a bouncing universe

TL;DR

This paper investigates the behavior of covariant perturbations during a cosmological bounce, revealing that linear perturbation theory breaks down near the bounce for certain fluid models.

Contribution

It introduces linearity parameters to assess the validity of linear perturbation theory near a bounce in covariant analysis, and computes shear tensor components for different fluid models.

Findings

Linearity conditions are violated near the bounce for radiationlike and dustlike fluids.

Linear evolution of density perturbations and gravitational waves has been previously established.

Shear tensor components induced by scalar and vector perturbations are calculated.

Abstract

In this paper we examine the validity of the linear perturbation theory near a bounce in the covariant analysis. Some linearity parameters are defined to set up conditions for a linear theory. Linear evolution of density perturbation and gravitational waves have been computed previously. We have calculated the vector and scalar induced parts of the shear tensor. For radiationlike and dustlike single fluid dominated collapsing Friedmann-Lemaitre-Robertson-Walker background it is shown that the linearity conditions are not satisfied near a bounce.