Primordial gravitational waves and curvature perturbations induced energy density perturbation

TL;DR

This paper investigates how primordial gravitational waves influence second-order scalar and energy density perturbations during the radiation era, providing explicit formulas and analyzing their effects with various primordial spectra.

Contribution

It presents explicit expressions for second-order scalar perturbations and explores the significant impact of primordial gravitational waves on energy density perturbations.

Findings

Primordial gravitational waves can significantly affect second-order energy density perturbations.

Explicit kernel functions and power spectra for second-order scalar perturbations are derived.

The impact varies with different primordial power spectra.

Abstract

We study the second order scalar and density perturbations generated by the Gaussian curvature perturbations and primordial gravitational waves in the radiation-dominated era. After presenting all the possible second-order source terms, we obtain the explicit expressions of the kernel functions and the power spectra of the second order scalar perturbations. It shows that the primordial gravitational waves might affect the second order energy density perturbation significantly. The effects of the primordial gravitational waves are studied in terms of different kinds of primordial power spectra.