We study whether the signal seen by pulsar timing arrays (PTAs) may originate from gravitational waves (GWs) induced by large primordial perturbations. Such perturbations may be accompanied by a sizable primordial black hole (PBH) abundance. We improve existing analyses and show that PBH overproduction disfavors Gaussian scenarios for scalar-induced GWs at $2\sigma$ and single-field inflationary scenarios, accounting for non-Gaussianity, at $3\sigma$ as the explanation of the most constraining NANOGrav 15-year data. This tension can be relaxed in models where non-Gaussianities suppress the PBH abundance. On the flip side, the PTA data does not constrain the abundance of PBHs.

• Received 4 July 2023
• Accepted 19 September 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.201401