Dynamics of Peccei-Quinn breaking field after inflation and axion isocurvature perturbations

The Peccei-Quinn mechanism suffers from the problem of the isocurvature perturbations. The isocurvature perturbations are suppressed if the Peccei-Quinn breaking scale is large during inflation. The oscillation of the Peccei-Quinn breaking field after inflation, however, leads to the formation of domain walls due to the parametric resonance effect. In this paper, we discuss the evolution of the Peccei-Quinn breaking field after inflation in detail, and propose a model where the parametric resonance is ineffective and hence domain walls are not formed. We also discuss consistency of our model with supersymmetric theory