# Pulsar Timing Array Constraints on the Induced Gravitational Waves

## TL;DR

This paper investigates how primordial black holes and their associated gravitational waves, detectable by pulsar timing arrays, can constrain early universe models, especially considering non-Gaussian curvature perturbations.

## Contribution

It demonstrates that non-Gaussianity in curvature perturbations can alleviate tensions between induced gravitational wave predictions and PTA constraints.

## Key findings

- Induced GWs from primordial black holes are in mild tension with current PTA constraints.
- Non-Gaussianity with $f_{NL} extgreater 10$ can relax this tension.
- Future observations by the Square Kilometer Array will be able to detect these GWs within a decade.

## Abstract

If the black holes detected by LIGO/VIRGO are primordial black holes (PBHs) sourcing from a large primordial curvature perturbation on small scales, the corresponding induced gravitational waves (GWs) would peak at nanohertz that is detectable by the current and future observations of pulsar timing array (PTA). In this paper we show that with the mass function estimated from the merger rate of LIGO O1 and O2 events, the induced GWs from such a curvature perturbation with a Gaussian narrow peak at some small scale would be in a seemingly mild tension with current constraints from PTA. However, if the curvature perturbation is of local-type non-Gaussianity with a non-linear parameter $f_\text{NL}\gtrsim\mathcal{O}(10)$, the tension could be relieved. Nevertheless, such an induced GWs must be detectable by the Square Kilometer Array in a decade or less.