  Axions differ from the other cold dark matter candidates in that they form a
degenerate Bose gas. It is shown that their huge quantum degeneracy and large
correlation length cause cold dark matter axions to thermalize through
gravitational self-interactions when the photon temperature reaches
approximately 500 eV. When they thermalize, the axions form a Bose-Einstein
condensate. Their thermalization occurs in a regime, herein called the
`condensed regime', where the Boltzmann equation is not valid because the
energy dispersion of the particles is smaller than their interaction rate. We
derive analytical expressions for the thermalization rate of particles in the
condensed regime, and check the validity of these expressions by numerical
simulation of a toy model. We revisit axion cosmology in light of axion
Bose-Einstein condensation. It is shown that axions are indistinguishable from
ordinary cold dark matter on all scales of observational interest, except when
they thermalize or rethermalize. The rethermalization of axions that are about
to fall in a galactic potential well causes them to acquire net overall
rotation as they go to the lowest energy state consistent with the total
angular momentum they acquired by tidal torquing. This phenomenon explains the
occurrence of caustic rings of dark matter in galactic halos. We find that
photons may reach thermal contact with axions and investigate the implications
of this possibility for the measurements of cosmological parameters.
