Eternal inflation in light of Wheeler-DeWitt equation

TL;DR

This paper explores how the Wheeler-DeWitt equation influences the conditions for eternal inflation, revealing a tower of power spectra and new bounds on inflation parameters, especially considering higher quantum excitations.

Contribution

It introduces a non-perturbative approach using the Wheeler-DeWitt equation to derive power spectra and bounds for eternal inflation, including effects of higher quantum states.

Findings

Derived a tower of power spectra not seen in perturbative methods.

Established new bounds on the slow-roll parameter for eternal inflation.

Showed that higher quantum excitations relax the conditions for eternal inflation.

Abstract

The Wheeler-DeWitt equation provides the probability distribution for the curvature perturbation, the gauge invariant quantum fluctuation of the inflaton. From this, we can find a tower of power spectra which is not found in a perturbative approach. Since the power spectrum for the modes that cross the horizon contributes to the uncertainty in the classical inflaton displacement, we obtain new conditions for eternal inflation. In the presence of the patch in the higher excitations, the bound on the slow-roll parameter allowing eternal inflation is given by at most $\epsilon \lesssim (2n+1)(H/m_{\rm Pl})^2$ with $n$ integer indicating the quantum number labelling the excitation. For large $n$, the bound on $\epsilon$ is relaxed such that eternal inflation can take place with even larger value of $\epsilon$. While the second law of thermodynamics implies that $n=0$ state is preferred, we cannot ignore such large $n$ effect since the nonlinear interaction inducing transitions to the $n=0$ state is suppressed.