Analytic solutions of scalar perturbations induced by scalar perturbations

Abstract

We study scalar perturbations induced by scalar perturbations through the non-linear interaction appearing at second order in perturbations. We derive analytic solutions of the induced scalar perturbations in a perfect fluid. In particular, we consider the perturbations in a radiation-dominated era and a matter-dominated era. With the analytic solutions, we also discuss the power spectra of the induced perturbations.

Comments: 37 pages, 7 figures, v2: version published in JCAP, paragraph structure changed