  We present analytic solutions to the spatially homogeneous axion field
equation, using a model potential which strongly resembles the $(1-\cos
\theta)$ standard anharmonic potential. We find that the anharmonicity
amplifies early universe axion density fluctuations, but only significantly so
for relatively large initial misalignment angles. Enhancements of $\sim$
(2,3,4,13) result for $\theta_{\rm in}\sim (0.85,0.90,0.95,0.99)\times\pi$. The
large $\theta$ result agrees with Lyth, and so validates his approximations.
