Second Order Gauge-Invariant Perturbations during Inflation
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.
Cite
@article{arxiv.gr-qc/0604081,
title = {Second Order Gauge-Invariant Perturbations during Inflation},
author = {F. Finelli and G. Marozzi and G. P. Vacca and G. Venturi},
journal= {arXiv preprint arXiv:gr-qc/0604081},
year = {2008}
}
Comments
17 pages, 6 figures. Final version to appear in Phys. Rev. D