Inflationary Reheating Classes via Spectral Methods
Bruce A. Bassett
Abstract
Inflationary reheating is almost completely controlled by the Floquet indices, μk. Using spectral theory we demonstrate that the stability bands (where μk = 0) of the Mathieu and Lam\'e equations are destroyed even in Minkowski spacetime, leaving a fractal Cantor set or a measure zero set of stable modes in the cases where the inflaton evolves in an almost-periodic or stochastic manner respectively. These two types of potential model the expected multi-field and quantum backreaction effects during reheating.
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