The general solution at large scale for second order perturbations in a scalar field dominated universe

摘要

In this paper we consider second order perturbations of a flat Friedmann-Lema?tre universe whose stress-energy content is a single minimally coupled scalar field with an arbi-trary potential. We derive the general solution of the perturbed Einstein equations in explicit form for this class of models when the perturbations are in the super-horizon regime. As a by-product we obtain a new conserved quantity for long wavelength perturbations of a single scalar field at second order.