A short note on the curvature perturbation at second order

Abstract

Working with perturbations about an FLRW spacetime, we compute the gauge-invariant curvature perturbation to second order solely in terms of scalar field fluctuations. Using the curvature perturbation on uniform density hypersurfaces as our starting point, we give our results in terms of field fluctuations in the flat gauge, incorporating both large and small scale behaviour. For ease of future numerical implementation we give our result in terms of the scalar field fluctuations and their time derivatives.

arXiv comment10 pages; v2: 11 pgs, added appendix, typos corrected. version to appear in Class. Quantum Grav

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• Deriving super-horizon curvature perturbations from the dynamics of preheating
• Non-linear effects in early Universe cosmology
• Non-Gaussianity after many-field reheating