Title: Scrutinizing the Primordial Black Holes Interpretation of PTA Gravitational Waves and JWST Early Galaxies

Abstract: Recent observations have granted to us two unique insights into the early universe: the presence of a low-frequency stochastic gravitational wave background detected by the NANOGrav and Pulsar Timing Array (PTA) experiments and the emergence of unusually massive galaxy candidates at high redshifts reported by the James Webb Space Telescope (JWST). In this letter, we consider the possibility that both observations have a common origin, namely primordial black holes (PBHs) in the mass range between $10^{6}~M_{\odot}$ and $10^{13}~M_{\odot}$. While superheavy PBHs act as seeds for accelerated galaxy formation capable of explaining the JWST extreme galaxies, they can also form binary mergers that source gravitational waves which can be potentially identified as the PTA signal. The analysis is performed taking into account the constraints on the relevant region of the PBH parameter space including the novel bound imposed by the Ultraviolet Luminosity Function of galaxies observed by the Hubble Space Telescope. We conclude that PTA's and JWST's interpretations in terms of PBH binary mergers and Poissonian gas of PBHs, respectively, are strongly excluded.