Damping mechanisms for coherent oscillations of axions

It has been proposed that the ‘‘mass turn-on’’ of the axion field in the early Universe could have set that field into a large-amplitude coherent oscillation. We give here a general analysis of damping mechanisms for field oscillations of this nature which are operative during an era of ‘‘mass turn-on.’’ A thermal-damping mechanism is analyzed in detail. Order-of-magnitude estimates indicate that the mechanism could possibly be important for axions if the mass turn-on rate is very large near the QCD temperature. If part of the mass turn-on occurs in association with a phase transition, a similar damping mechanism due to phase nonequilibria could be operative. Furthermore, supercooling could lead to a very effective damping mechanism. In addition, phase separation could result in scattering of the axions and destruction of their coherence. Other damping mechanisms of a more mechanical nature are also analyzed. We conclude that the upper limit of ∼${10}^{12}$ GeV for the vacuum expectation value associated with the spontaneous breaking of Peccei-Quinn symmetry—previously derived from arguments concerning cosmological overproduction of coherent axions—should not be considered as firm.