Second order cosmological perturbations: simplified gauge change formulas

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.

21 pages, no figures

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• Scalar field evolution at background and perturbation levels for a broad class of potentials
• Second order cosmological perturbations: new conserved quantities and the general solution at super-horizon scale
• The general solution at large scale for second order perturbations in a scalar field dominated universe