Implications for the non-Gaussianity of curvature perturbation from pulsar timing arrays

TL;DR

This paper uses pulsar timing array data to constrain the non-Gaussianity of curvature perturbations, providing the first such limits and exploring implications for inflation models and primordial black hole production.

Contribution

It presents the first constraints on the non-Gaussianity parameter from PTA data assuming scalar-induced gravitational waves.

Findings

Constraint |F_NL| ≲ 13.9 for lognormal spectrum

F_NL range -13.9 to -0.1 to avoid primordial black holes

Future space-based GW detectors can further probe non-Gaussianity

Abstract

The recently released data by pulsar timing array (PTA) collaborations present strong evidence for a stochastic signal consistent with a gravitational-wave background. Assuming this signal originates from scalar-induced gravitational waves, we jointly use the PTA data from the NANOGrav 15-yr data set, PPTA DR3, and EPTA DR2 to probe the small-scale non-Gaussianity. We put the first-ever constraint on the non-Gaussianity parameter, finding $|F_\mathrm{NL}|\lesssim 13.9$ for a lognormal power spectrum of the curvature perturbations. Furthermore, we obtain $-13.9 \lesssim F_\mathrm{NL}\lesssim -0.1$ to prevent excessive production of primordial black holes. Moreover, the multi-band observations with the space-borne gravitational-wave detectors, such as LISA/Taiji/TianQin, will provide a complementary investigation of primordial non-Gaussianity. Our findings pave the way to constrain inflation models with PTA data.