The curvature perturbation at second order

Abstract

We give an explicit relation, up to second-order terms, between scalar-field fluctuations defined on spatially-flat slices and the curvature perturbation on uniform-density slices. This expression is a necessary ingredient for calculating observable quantities at second-order and beyond in multiple-field inflation. We show that traditional cosmological perturbation theory and the `separate universe' approach yield equivalent expressions for superhorizon wavenumbers, and in particular that all nonlocal terms can be eliminated from the perturbation-theory expressions.

16 pages, no figures. This is an author-created, un-copyedited version of an article published in JCAP. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1475-7516/2015/02/040. v3: Updated to match version published in JCAP

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• Non-gaussianity from the second-order cosmological perturbation
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• Inflationary perturbation theory is geometrical optics in phase space
• Non-Gaussian Correlations Outside the Horizon
• Transport equations for the inflationary trispectrum
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