Bose-Einstein condensation of the classical axion field in cosmology?

The axion is a motivated cold dark matter candidate, which it would be interesting to distinguish from weakly interacting massive particles. Sikivie has suggested that axions could behave differently during non-linear galaxy evolution, if they form a Bose-Einstein condensate, and argues that "gravitational thermalisation" drives them to a Bose-Einstein condensate during the radiation dominated era. Using classical equations of motion during linear structure formation, we explore whether the gravitational interactions of axions can generate enough entropy. At linear order in G(N), we interpret that the principle activities of gravity are to expand the Universe and grow density fluctuations. To quantify the rate of entropy creation we use the anisotropic stress to estimate a short dissipation scale for axions which does not confirm previous estimates of their gravitational thermalisation rate.