Friction on ALP domain walls and gravitational waves

Abstract: We study the early Universe evolution of axion-like particle (ALP) domain walls taking into account the effect of friction from particles in the surrounding plasma, including the case of particles in thermal equilibrium and frozen out species. We characterize the friction force from interactions within the ALP effective theory, providing new results for the fermion contribution as well as identifying simple conditions for friction to be relevant during the domain wall life time. When friction dominates, the domain wall network departs from the standard scaling regime and the corresponding gravitational wave emission is affected. As a relevant example, we show how this can be the case for ALP domain walls emitting at the typical frequencies of Pulsar Timing Array experiments, when the ALP couples to the SM leptons. We then move to a general exploration of the gravitational wave prospects in the ALP parameter space. We finally illustrate how the gravitational wave signal from ALP domain walls is correlated with the quality of the underlying $U(1)$ symmetry.