Spectrum of third-order tensor perturbations induced by excited scalar fields

TL;DR

This paper calculates the third-order gravitational wave spectrum generated during inflation by excited scalar fields, revealing that it can dominate over the second-order spectrum and potentially break perturbation theory.

Contribution

First calculation of the third-order gravitational wave spectrum sourced by amplified scalar fields during inflation using the in-in formalism.

Findings

Third-order spectrum increases faster than second-order with amplification.

Third-order spectrum can dominate for detectable gravitational waves.

Perturbation theory may break down under strong amplification.

Abstract

We calculate for the first time the third-order spectrum of gravitational waves sourced by the amplified scalar field perturbations during inflation using the in-in formalism, and discuss the conditions for the third-order spectrum to be smaller than the second-order one. Assuming an exponential growth of the sub-horizon modes of the scalar field perturbations, we find that the third-order spectrum increases faster than the second-order one as the amplification of the field perturbations increases, and thus the third-order spectrum dominates for detectable gravitational waves, which indicates that the perturbation theory breakdowns.