# When Primordial Black Holes from Sound Speed Resonance Meet a Stochastic Background of Gravitational Waves

## TL;DR

This paper investigates how sound speed resonance during inflation can produce primordial black holes and a distinctive stochastic gravitational wave background, offering potential observational signatures for multi-messenger astronomy.

## Contribution

It introduces a novel mechanism linking sound speed resonance to PBH formation and analyzes the resulting gravitational wave spectrum from both inflation and radiation eras.

## Key findings

- Induced GWs during inflation can be significant at certain frequencies due to resonance.
- The GW energy spectrum has a specific profile with observable features.
- Joint detection prospects for PBHs via electromagnetic signals and gravitational waves.

## Abstract

As potential candidates of dark matter, primordial black holes (PBHs) are within the core scopes of various astronomical observations. In light of the explosive development of gravitational wave (GW) and radio astronomy, we thoroughly analyze a stochastic background of cosmological GWs, induced by over large primordial density perturbations, with several spikes that was inspired by the sound speed resonance effect and can predict a particular pattern on the mass spectrum of PBHs. With a specific mechanicsm for PBHs formation, we for the first time perform the study of such induced GWs that originate from both the inflationary era and the radiation-dominated phase. We report that, besides the traditional process of generating GWs during the radiation-dominated phase, the contribution of the induced GWs in the sub-Hubble regime during inflation can become significant at critical frequency band because of a narrow resonance effect. All contributions sum together to yield a specific profile of the energy spectrum of GWs that can be of observable interest in forthcoming astronomical experiments. Our study shed light on the possible joint probe of PBHs via various observational windows of multi-messenger astronomy, including the search for electromagnetic effects with astronomical telescopes and the stochastic background of relic GWs with GW instruments.