Primordial gravitational wave background as a probe of primordial black holes

We study the formation of primordial black holes (PBHs) from the collapse of density perturbations induced by primordial gravitational waves (PGWs). The PGWs' interpretation of the stochastic gravitational wave background detected by the pulsar timing array corresponds to PBH formation in the mass range $[{10}^{\ensuremath{-}12}\ensuremath{-}{10}^{\ensuremath{-}3}]{M}_{\ensuremath{\bigodot}}$. Importantly, our analysis shows that PGWs' interpretation of recent pulsar timing array data remains viable, as it does not lead to PBH overproduction. We derive the amplitude of PGWs by leveraging existing constraints on the PBH abundance across a wide mass range. Notably, these constrained amplitudes predict stochastic gravitational wave background signals that would be detectable by future gravitational wave observatories.