A not so short note on the Klein-Gordon equation at second order

Abstract

We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon equation at second order in closed form in terms of gauge-invariant perturbations of the fields in the uniform curvature gauge. We also give a simplified form of the Klein-Gordon equation using the slow-roll approximation.

12 pages, revtex; V2: minor changes, typos and errors corrected (list of corrections added to appendix), conclusions unchanged; V3: minor changes, corresponds to published version; V4: minor changes, errors corrected; V5: minor changes, errors corrected

References in corpus (2)

• Non-gaussianity from the second-order cosmological perturbation
• A numerical study of non-gaussianity in the curvaton scenario

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