Early-Universe Simulations of the Cosmological Axion

Ultracompact dark matter (DM) minihalos at masses at and below $10^{-12}$ $M_\odot$ arise in axion DM models where the Peccei-Quinn (PQ) symmetry is broken after inflation. The minihalos arise from density perturbations that are generated from the non-trivial axion self interactions during and shortly after the collapse of the axion-string and domain-wall network. We perform high-resolution simulations of this scenario starting at the epoch before the PQ phase transition and ending at matter-radiation equality. We characterize the spectrum of primordial perturbations that are generated and comment on implications for efforts to detect axion DM. We also measure the DM density at different simulated masses and argue that the correct DM density is obtained for $m_a = 25.2 \pm 11.0$ $\mu\mathrm{eV}$.