Second order cosmological perturbations: gauge change and gauge invariants

In this paper we present a new formulation of the change of gauge formulas at second order in cosmological perturbation theory which unifies, simplifies and extends previous seemingly disparate results concerning change of gauge. Our approach is based on defining new second order perturbation variables by adding a multiple of the square of the corresponding first order variable 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 perturbations in the super-horizon regime in a number of ways, and lead to new conserved quantities.