# Probing Primordial-Black-Hole Dark Matter with Scalar Induced Gravitational Waves

## TL;DR

This paper investigates how third-order corrections in scalar-induced gravitational waves can enhance detection prospects and constrain primordial black hole dark matter models, especially with upcoming LISA and PTA observations.

## Contribution

It calculates third-order corrections to scalar-induced GWs, showing increased amplitude and extended frequency cutoff, impacting PBH dark matter constraints and detection strategies.

## Key findings

- Third-order corrections increase GW signal amplitude by about 10%.
- Extended cutoff frequency from 2k* to 3k* broadens detectable PBH mass range.
- Null GW detections can exclude PBHs as all dark matter and link GW events to PBHs.

## Abstract

The possibility that primordial black holes (PBHs) represent all of the dark matter (DM) in the Universe and explain the coalescences of binary black holes detected by LIGO/Virgo has attracted a lot of attention. PBHs are generated by the enhancement of scalar perturbations which inevitably produce the induced gravitational waves (GWs). We calculate the induced GWs up to the third-order correction which not only enhances the amplitude of induced GWs, but also extends the cutoff frequency from $2k_*$ to $3k_*$. Such effects of the third-order correction lead to an around $10\%$ increase of the signal-to-noise ratio (SNR) for both LISA and pulsar timing array (PTA) observations, and significantly widen the mass range of PBHs in the stellar mass window accompanying detectable induced GWs for PTA observations including IPTA, FAST and SKA. On the other hand, the null detections of the induced GWs by LISA and PTA experiments will exclude the possibility that all of the DM is comprised of PBHs and the GW events detected by LIGO/Virgo are generated by PBHs.