Extension of DeWitt-kernel construction to inhomogeneous perturbations

Establish whether the exact DeWitt-kernel construction for minisuperspace quantum cosmology survives the inclusion of inhomogeneous perturbations, particularly in light of the perturbative ill-behavior of the DeWitt wave function of general relativity.

Background

The paper constructs exact positive-lapse Green functions and whole-real-line group-averaging kernels for several homogeneous and isotropic minisuperspace models. These kernels implement the DeWitt boundary condition by restricting the quantum configuration variable to the positive half-line and imposing a Dirichlet condition at the singular geometry.

The authors note that the DeWitt condition has limitations beyond minisuperspace: vanishing of the wave function at the singularity does not by itself ensure finite curvature-invariant expectation values, and the DeWitt wave function of full general relativity is known to be perturbatively ill-behaved when inhomogeneous degrees of freedom are included. It therefore remains unresolved whether the exact kernel construction and its Dirichlet/self-adjoint-extension framework can be generalized to inhomogeneous perturbations.