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Second Order Gauge-Invariant Perturbations during Inflation

F. Finelli·G. Marozzi·G. P. Vacca·G. Venturi
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Abstract

The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second order gauge invariant expressions for the curvature are considered. We evaluate perturbatively one of these second order curvature fluctuations and a second order gauge invariant scalar field fluctuation during the slow-roll stage of a massive chaotic inflationary scenario, taking into account the deviation from a pure de Sitter evolution and considering only the contribution of super-Hubble perturbations in mode-mode coupling. The spectra resulting from their contribution to the second order quantum correlation function are nearly scale-invariant, with additional logarithmic corrections to the first order spectrum. For all scales of interest the amplitude of these spectra depend on the total number of e-folds. We find, on comparing first and second order perturbation results, an upper limit to the total number of e-folds beyond which the two orders are comparable.

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F. Finelli, G. Marozzi, G. P. Vacca, G. Venturi. 2006-10-31. Second Order Gauge-Invariant Perturbations during Inflation. https://doi.org/10.1103/physrevd.74.083522

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