Practical tools for third order cosmological perturbations

TL;DR

This paper develops practical tools for third order cosmological perturbation theory, including gauge transformations, invariant quantities, and detailed evolution equations for various perturbation types.

Contribution

It provides comprehensive derivations of third order gauge transformation rules, gauge invariant variables, and detailed evolution equations for scalar, vector, and tensor perturbations.

Findings

Derived third order gauge transformation rules

Constructed third order gauge invariant quantities

Presented full second order tensor components and evolution equations

Abstract

We discuss cosmological perturbation theory at third order, deriving the gauge transformation rules for metric and matter perturbations, and constructing third order gauge invariant quantities. We present the Einstein tensor components, the evolution equations for a perfect fluid, and the Klein-Gordon equation at third order, including scalar, vector and tensor perturbations. In doing so, we also give all second order tensor components and evolution equations in full, exhilarating generality.