Inflationary Reheating Classes via Spectral Methods

Inflationary reheating is almost completely controlled by the Floquet indices, ${\mu }_k$. Using spectral theory we demonstrate that the stability bands (where ${\mu }_k=0$) 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.