  We show that cold dark matter axions thermalize and form a Bose-Einstein
condensate. We obtain the axion state in a homogeneous and isotropic universe,
and derive the equations governing small axion perturbations. Because they form
a BEC, axions differ from ordinary cold dark matter in the non-linear regime of
structure formation and upon entering the horizon. Axion BEC provides a
mechanism for the production of net overall rotation in dark matter halos, and
for the alignment of cosmic microwave anisotropy multipoles.
