Axion Dissipation Through the Mixing of Goldstone Bosons
  By coupling axions strongly to a hidden sector, the energy density in coherent axions may be converted to radiative degrees of freedom, alleviating the ``axion energy crisis''. The strong coupling is achieved by mixing the axion and some other Goldstone boson through their kinetic energy terms, in a manner reminiscent of paraphoton models. Even with the strong coupling it proves difficult to relax the axion energy density through particle absorption, due to the derivative nature of Goldstone boson couplings and the effect of back reactions on the evolution of the axion number density. However, the distribution of other particle species in the hidden sector will be driven from equilibrium by the axion field oscillations. Restoration of thermal equilibrium results in energy being transferred from the axions to massless particles, where it can redshift harmlessly without causing any cosmological problems. 
K.S. Babu, S.M. Barr and D. Seckel