Cosmic axion thermalization
  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. 
O. Erken, P. Sikivie, H. Tam and Q. Yang
astro-ph.CO cond-mat.stat-mech hep-ph