Resonant multiple peaks in the induced gravitational waves

Abstract

We identify analytically a multiple-peak structure in the energy-density spectrum of induced gravitational waves (GWs) generated at second-order from a primordial scalar perturbations also with multiple($n$) peaks at small scales $k_{*i}$. The energy-density spectrum of induced GWs exhibits at most $C_{n+1}^2$ and at least $n$ peaks at wave-vectors $k_{ij}\equiv(k_{*i}+k_{*j})/\sqrt{3}$ due to resonant amplification, and, under the narrow-width approximation, it contains an universal factor that can be interpreted as a result of momentum conservation. We also extend these discussions to the case of non-Gaussian perturbations.