Post-Inflation Reheating in an Expanding Universe

An analytic means of studying the resonant decay of the inflaton field is developed for the case of background expansion, $H \neq 0$. It is shown that the parametric resonance in the inflaton's decay need not disappear when the expansion of the universe is taken into account, although the total number of particles produced is fewer than in the $H \simeq 0$ case.