Analytic solutions of scalar perturbations induced by scalar perturbations

Understand

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.