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 Lamé 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 back reaction effects during reheating.