Analytic solutions of scalar perturbations induced by scalar perturbations

TL;DR

This paper derives analytic solutions for scalar perturbations induced by scalar perturbations during radiation- and matter-dominated eras, providing insights into their power spectra and non-linear interactions.

Contribution

It presents the first analytic solutions for second-order induced scalar perturbations in a perfect fluid during key cosmological eras.

Findings

Analytic solutions for induced scalar perturbations in radiation and matter eras.

Discussion of the power spectra of the induced perturbations.

Insights into non-linear interactions at second order.

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.