A Common Origin for Nano-Hz Gravitational Wave Background and Black Hole Merger Events

We explore the potential primordial connection between the black hole merger events detected by LIGO and the nano-Hz stochastic gravitational wave background observed by pulsar timing arrays. We propose an innovative mechanism for the formation of primordial black holes, suggesting that the Poisson fluctuations within the domain wall network can give rise to horizon-sized overdense regions. Our results indicate a plausible common origin for gravitational wave observations in two different frequency bands, potentially linked to the annihilation of the domain wall network at the QCD scale, while accounting for the accretion effects on primordial black holes. Furthermore, we demonstrate that the bias potential induced by the QCD instanton effect may naturally facilitate the annihilation of the domain wall network during the QCD phase transition. Additionally, our scenario can yield the correct axion dark matter relic abundance, particularly if realized within the clockwork axion framework.