Primordial Black Holes from Axion Domain Wall Collapse

The QCD axion can solve the Strong CP Problem and be the dark matter of our universe. If the PQ symmetry breaking scale associated with the axion is below the inflationary reheating temperature, axion strings and domain walls populate the universe. Most of these strings and walls decay away into axion dark matter, but a small subset of the walls will be self-enclosed surfaces that are not attached to any strings. These enclosed walls can collapse in on themselves, compressing a large amount of energy into a small volume and potentially forming primordial black holes (PBHs). We study the number density and dynamics of these self-enclosed walls, taking into account their size distribution, Hubble expansion, asphericities, and all stages of domain wall dynamics using a combination of semi-analytic and numerical approaches. We find that axion models with a high axion decay constant $f_a$, such as those of interest in early matter-dominated cosmologies, yield a PBH abundance potentially observable by future gravitational lensing surveys. We note that the formalism developed here is also useful for predicting relic PBH abundances in other models that exhibit unstable domain walls.