Is the axionic dark matter an equilibrium system?
  We consider an axionic dark matter model with a modified periodic potential
for the pseudoscalar field in the framework of the axionic extension of the
Einstein-aether theory. The modified potential is assumed to be equipped by the
guiding function, which depends on the expansion scalar constructed as the
trace of the covariant derivative of the aether velocity four-vector. The
equilibrium state of the axion field is defined as the state, for which the
modified potential itself and its first derivative with respect to the
pseudoscalar field are equal to zero. We apply the developed formalism to the
homogeneous isotropic cosmological model, and find the basic function, which
describes the equilibrium state of the axionic dark matter in the expanding
Universe.
