Acoustic Misalignment Mechanism for Axion Dark Matter

A rotation in the field space of a complex scalar field corresponds to a Bose-Einstein condensation of $U(1)$ charges. We point out that fluctuations in this rotating condensate exhibit sound-wave modes, which can be excited by cosmic perturbations and identified with axion fluctuations once the $U(1)$ charge condensate has been sufficiently diluted by cosmic expansion. We consider the possibility that these axion fluctuations constitute dark matter and develop a formalism to compute its abundance. We carefully account for the growth of fluctuations during the epoch where the complex scalar field rotates on the body of the potential and possible nonlinear evolution when the fluctuations become non-relativistic. We find that the resultant dark matter abundance can exceed the conventional and kinetic misalignment contributions if the radial direction of the complex scalar field is sufficiently heavy. The axion dark matter may also be warm enough to leave imprints on structure formation. We discuss the implications of this novel dark matter production mechanism -- {\it acoustic misalignment mechanism} -- for the axion rotation cosmology, including kination domination and baryogenesis from axion rotation, as well as for axion searches.