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

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 $\mathrm{\mid }{F}_{\mathrm{N}\mathrm{L}}\mathrm{\mid }\lesssim 13.9$ for a lognormal power spectrum of the curvature perturbations. Furthermore, we obtain $-13.9\lesssim F_{\mathrm{N}\mathrm{L}}\lesssim -0.1$ 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.