# Resonant multiple peaks in the induced gravitational waves

## TL;DR

This paper analytically demonstrates that induced gravitational waves from primordial scalar perturbations with multiple peaks exhibit a multi-peak structure in their energy-density spectrum, with resonance effects leading to predictable peak patterns.

## Contribution

It provides an analytical framework for understanding the multi-peak structure in induced GWs from multi-peaked primordial perturbations, including non-Gaussian cases.

## Key findings

- The spectrum shows at most C(n+1,2) peaks due to resonance.
- The peaks occur at wave-vectors (k_{*i}+k_{*j})/√3.
- Universal factors relate to momentum conservation under narrow-width approximation.

## 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.