Domain wall interpretation of the PTA signal confronting black hole overproduction

Recently, Pulsar Timing Array (PTA) Collaborations have detected a stochastic gravitational wave background (SGWB) at nano-Hz frequencies, with domain wall networks (DWs) proposed as potential sources. To be cosmologically viable, they must annihilate before dominating the Universe energy budget, thus generating a SGWB. While subhorizon DWs shrink and decay rapidly, causality requires DWs with superhorizon size to continue growing until they reach the Hubble horizon. Those entering the latest can be heavier than a Hubble patch and collapse into primordial black holes (PBHs). We conduct a Bayesian analysis of the PTA signal, interpreting it as an outcome of SGWB from DW networks, with a prior ensuring no PBH overproduction. Our findings indicate that DWs result in the production of solar-mass PBHs. The binary mergers occurring within these PBHs generate a second SGWB in the kilo-Hz domain which could be observable in ongoing or planned Earth-based interferometers.