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 out that the flat potential is naturally obtained in a supersymmetric extension of the Peccei-Quinn model. If Peccei-Quinn breaking scale $F_a$ is about 10^{12} GeV, this model predicts anisotropies of cosmic microwave background radiation due to the axion isocurvature fluctuations which may be detectable in future observations. 
S. Kasuya, M. Kawasaki and T. Yanagida