Strongly broken Peccei-Quinn symmetry in the early Universe
  We consider QCD axion models where the Peccei-Quinn symmetry is badly broken
by a larger amount in the past than in the present, in order to avoid the axion
isocurvature problem. Specifically we study supersymmetric axion models where
the Peccei-Quinn symmetry is dynamically broken by either hidden gauge
interactions or the $SU(3)_c$ strong interactions whose dynamical scales are
temporarily enhanced by the dynamics of flat directions. The former scenario
predicts a large amount of self-interacting dark radiation as the hidden gauge
symmetry is weakly coupled in the present Universe. We also show that the
observed amount of baryon asymmetry can be generated by the QCD axion dynamics
via spontaneous baryogenesis. We briefly comment on the case in which the PQ
symmetry is broken by a non-minimal coupling to gravity.
