Studies of the motion and decay of axion walls bounded by strings

We discuss the appearance at the QCD phase transition, and the subsequent decay, of axion walls bounded by strings in $N=1$ axion models. We argue on intuitive grounds that the main decay mechanism is into barely relativistic axions. We present numerical simulations of the decay process. In these simulations, the decay happens immediately, in a time scale of order the light travel time, and the average energy of the radiated axions is $〈{\ensuremath{\omega}}_{a}〉\ensuremath{\simeq}{7m}_{a}$ for ${v}_{a}{/m}_{a}\ensuremath{\simeq}500.$ $〈{\ensuremath{\omega}}_{a}〉$ is found to increase approximately linearly with $\mathrm{ln}{(v}_{a}{/m}_{a}).$ Extrapolation of this behavior yields $〈{\ensuremath{\omega}}_{a}〉\ensuremath{\sim}{60m}_{a}$ in axion models of interest. We find that the contribution to the cosmological energy density of axions from wall decay is of the same order of magnitude as that from vacuum realignment, with however large uncertainties. The velocity dispersion of axions from wall decay is found to be larger, by a factor ${10}^{3}$ or so, than that of axions from vacuum realignment and string decay. We discuss the implications of this for the formation and evolution of axion miniclusters and for the direct detection of axion dark matter on Earth. Finally we discuss the cosmology of axion models with $N>1$ in which the domain wall problem is solved by introducing a small ${U}_{\mathrm{PQ}}$(1) breaking interaction. We find that in this case the walls decay into gravitational waves.