Preheating and the Einstein field equations

We inaugurate a framework for studying preheating and parametric resonance after inflation without resorting to any approximations, either in gravitational perturbation theory or in the classical evolution of the field(s). We do this by numerically solving the Einstein field equations in the post-inflationary universe. In this paper we show how to compare our results to those of gauge invariant perturbation theory. We then verify the analysis of Finelli and Brandenberger (hep-ph/9809490) of super-horizon modes in $m^2{\phi }^2$ inflation, showing that they are not amplified by resonant effects. Lastly, we make a preliminary survey of the nonlinear couplings between modes, which will be important in models where the primordial metric perturbations undergo parametric amplification.