Cosmological axion problem in chaotic inflationary universe

We investigate two cosmological axion problems (isocurvature fluctuations and domain-wall formation) in chaotic inflationary universe. It is believed that these problems are solved if potential for the Peccei-Quinn scalar field is very flat. However, we find that too many domain walls are produced through parametric resonance decay of the Peccei-Quinn scalar field. Only the axion model with N = 1 (N; QCD anomaly factor) is consistent with observations. We also point that the flat potential is naturally obtained in a supersymmetric extension of the Peccei-Quinn model. If Peccei-Quinn breaking scale Fa is about 1012 GeV, this model predicts anisotropies of cosmic microwave background radiation due to the axion isocurvature fluctuations which may be detectable in future observations.