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 106Β Mββ and
1013Β Mββ. While superheavy PBHs act as seeds of 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 so-called 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.Comment: 6+4 pages, 1+4 figure