Gauge-invariant perturbations at second order: multiple scalar fields on large scales

Abstract

We derive the governing equations for multiple scalar fields minimally coupled to gravity in a flat Friedmann-Robertson-Walker (FRW) background spacetime on large scales. We include scalar perturbations up to second order and write the equations in terms of physically transparent gauge-invariant variables at first and second order. This allows us to write the perturbed Klein-Gordon equation at second order solely in terms of the field fluctuations on flat slices at first and second order.

Comments: 16 pages, no figures, revtex4; v2: sign errors in Eqs. (4.16) and (7.6) corrected, application section added, typos corrected, reference added; v3: minor changes, as published version