Axion structure formation - I: the co-motion picture

Axion as dark matter is an increasingly important subject in astrophysics and cosmology. Experimental and observational searches are mounting across the mass spectrum of axion-like particles, many of which require detailed knowledge of axion structure over a wide range of scales. Current understanding of axion structures is far from complete, however, due largely to controversy in modeling the candidate's highly degenerate state. The series Axion Structure Formation seeks to develop a consistent model of QCD axion dark matter dynamics that follows their highly degenerate nature to the present using novel modeling techniques and sophisticated simulations. This inaugural paper presents the problem of describing many non-relativistic axions with minimal degrees of freedom and constructs a theory of axion infall for the limit of complete condensation. The derived model is shown to contain axion-specific dynamics not unlike the exchange-correlation influences experienced by identical fermions. Perturbative calculations are performed to explore the potential for imprints in early universe structures.