  We survey observational constraints on the parameter space of inflation and
axions and map out two allowed windows: the classic window and the inflationary
anthropic window. The cosmology of the latter is particularly interesting;
inflationary axion cosmology predicts the existence of isocurvature
fluctuations in the CMB, with an amplitude that grows with both the energy
scale of inflation and the fraction of dark matter in axions. Statistical
arguments favor a substantial value for the latter, and so current bounds on
isocurvature fluctuations imply tight constraints on inflation. For example, an
axion Peccei-Quinn scale of 10^16 GeV excludes any inflation model with energy
scale > 3.8*10^14 GeV (r > 2*10^(-9)) at 95% confidence, and so implies
negligible gravitational waves from inflation, but suggests appreciable
isocurvature fluctuations.
