Evolution and thermalization of dark matter axions in the condensed
  regime
  We discuss the possibility that dark matter axions form a Bose-Einstein
condensate (BEC) due to the gravitational self-interactions. The formation of
BEC occurs in the condensed regime, where the transition rate between different
momentum states is large compared to the energy exchanged in the transition.
The time evolution of the quantum state occupation number of axions in the
condensed regime is derived based on the in-in formalism. We recover the
expression for the thermalization rate due to self interaction of the axion
field, which was obtained in the other literature. It is also found that the
leading order contributions for interactions between axions and other species
vanish, which implies that the axion BEC does not give any significant
modifications on standard cosmological parameters.
