Flatons and Peccei-Quinn Symmetry

We study in detail a supersymmetric Peccei-Quinn model, which has a DFSZ and a KSVZ version. The fields breaking the Peccei-Quinn (PQ) symmetry correspond to flat directions (flaton fields) and have unsuppressed couplings when PQ symmetry is unbroken. The models have interesting particle physics phenomenology. The PQ scale is naturally generated through radiative corrections; also, in the DFSZ case the $\mu$ problem can be solved and neutrino masses can be generated. Cosmologically they lead to a short period of thermal inflation making the axion an excellent dark matter candidate if one of the flaton fields has a positive effective mass-squared at early times but with too low a density in the opposite case. A highly relativistic population of axions is produced by flaton decay during the subsequent reheating, whose density is constrained by nucleosynthesis. We evaluate all of the relevant reaction rates and evaluate the nucleosynthesis constraint. We find that the KSVZ model is practically ruled out, while the DFSZ model has a sizable allowed region of parameter space.