A Solvable Model for Anharmonic Evolution of Cosmic Axion Overdensitites

Abstract

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 ${\theta }_{\mathrm{in}}\sim (0.85,0.90,0.95,0.99)\times \pi$. The large $\theta$ result agrees with Lyth, and so validates his approximations.

Comments: VAND-TH-94-22; presented at the 7th Marcel Grossmann Meeting on General Relativity, Stanford U. July 24-29, 1994. 5 pages, Latex with three postscript figures and two World Sci macros appended