Preheating and the Einstein Field Equations

Abstract

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 evolution of the field(s). We do this by numerically solving the Einstein field equations in the post-inflationary universe. In this letter we show how to compare our results to those of gauge invariant perturbation theory. We then verify Finelli and Brandenberger's analysis (hep-ph/9809490) of super-horizon modes in $m^2φ^2$ 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.

Figures (3)

• Figure 1: The evolution of the $\Phi_1$ mode, with a wavelength $Z$, is plotted for $\epsilon=0.001$, After an initial transient decays the solution tends towards a constant, as expected for a super-horizon mode. The time is normalized so that $m=1$. For our choice of phase, only the imaginary part of $\Phi_1$ is excited.
• Figure 2: The evolution of $|\Phi_5|$ (upper) and $|\Phi_{10}|$ are plotted, for the nonlinear case of $\epsilon =.1$. In this case, there is a significant transfer of power to higher modes.
• Figure 3: Several modes of $\Phi$ are plotted with $\epsilon=0.05$ and $k=8$, and the perturbation given by equation (\ref{['pert2']}). Here, $\Phi_1$ is initially excited, but significant amounts of power are transferred to other modes.