Eternal inflation in light of Wheeler-DeWitt equation
  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.
