Post-inflationary reheating

We study the two field model for reheating based on the scalar inflaton field $\ensuremath{\varphi}$ and its interaction with another scalar field \ensuremath{\chi} through a Lagrangian term $\frac{1}{2}{g}^{2}{\ensuremath{\chi}}^{2}{\ensuremath{\varphi}}^{2},$ much investigated for parametric resonance or preheating. Attention is paid particularly to the quantum excitations of the inflaton field and the metric with a smooth transition from quantum to classical stochastic states, and with reheating followed right through from a specific inflation model to a state including a relativistic (radiation) fluid. The excitations of the metric (but not the inflaton or $\ensuremath{\chi})$ are treated perturbatively and the validity of this approach is assessed. For this model our work points to the possibility of the cosmic reheating period ending in a two-component state (one being the radiation fluid and the other nonthermalized inflaton relics) and also to \ensuremath{\zeta} (the curvature parameter for observed cosmic microwave background anisotropies) changing significantly during reheating with parametric resonance.