Second order cosmological perturbations: simplified gauge change formulas

TL;DR

This paper introduces a simplified and unified approach to gauge change formulas in second order cosmological perturbation theory, enhancing analysis and revealing new conserved quantities.

Contribution

It proposes new second order scalar perturbation variables that simplify gauge transformations and analysis of super-horizon scalar perturbations.

Findings

New gauge change formulas unify existing results.

Simplified variables facilitate super-horizon analysis.

Identification of new conserved quantities.

Abstract

In this paper we present a new formulation of the change of gauge formulas in second order cosmological perturbation theory which unifies and simplifies known results. Our approach is based on defining new second order scalar perturbation variables by adding a multiple of the square of the corresponding first order variables to each second order variable. A bonus is that these new perturbation variables are of broader significance in that they also simplify the analysis of second order scalar perturbations in the super-horizon regime in a number of ways, and lead to new conserved quantities.