  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.
