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

We calculate for the first time the third-order spectrum of gravitational waves sourced by the scalar field perturbations amplified during inflation using the in-in formalism and discuss the conditions for the third-order spectrum to be smaller than the second-order one. 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.