Second Order perturbation Theory: A covariant approach involving a barotropic equation of state

TL;DR

This paper develops a covariant, gauge-invariant formalism for analyzing second-order tensor perturbations in cosmology, particularly focusing on models with different equations of state and implications for CMB polarization.

Contribution

It introduces a novel analytical approach for second-order tensor perturbations in FLRW models with various equations of state, enhancing understanding of higher order effects.

Findings

Potential to examine CMB polarization from higher order perturbations

Formalism applicable to different equations of state

Analytical method for pure second-order tensor perturbations

Abstract

We present a covariant and gauge invariant formalism suited to the study of second-order effects associated with higher order tensor perturbations. The analytical method we have developed enables us to characterize pure second-order tensor perturbations about FLRW model having different kinds of equations of state. Our analysis of the radiation case suggests that it may be feasible to examine the CMB polarization arising from higher order perturbations.