Mirror World and Axion: Relaxing Cosmological Bounds
  The cosmological (upper) limit on the Peccei-Quinn constant, related to the primordial oscillations of the axion field, can be relaxed for a mirror axion model. The simple reason is that the mirror world is colder and so the behavior of the axion temperature-dependent mass is dominated by the contribution from the mirror sector. So the coherent oscillations start earlier and correspondingly the axion mass density \Omega_a h^2 is reduced. 
Giannotti Maurizio