Semiclassical solutions of generalized Wheeler-DeWitt cosmology

TL;DR

This paper extends Wheeler-DeWitt cosmology with interaction terms, develops perturbative methods, and explores connections to quantum gravity, providing exact solutions and first-order corrections for a closed universe model.

Contribution

It introduces a framework for adding and analyzing interaction terms in Wheeler-DeWitt cosmology, including exact and perturbative solutions, linking semiclassical cosmology to quantum gravity.

Findings

Derived the exact Feynman propagator via conformal transformation.

Computed first-order perturbative corrections for stochastic interactions.

Obtained Green's kernel for time-independent interactions.

Abstract

We consider an extension of WDW minisuperpace cosmology with additional interaction terms that preserve the linear structure of the theory. General perturbative methods are developed and applied to known semiclassical solutions for a closed Universe filled with a massless scalar. The exact Feynman propagator of the free theory is derived by means of a conformal transformation in minisuperspace. As an example, a stochastic interaction term is considered and first order perturbative corrections are computed. It is argued that such an interaction can be used to describe the interaction of the cosmological background with the microscopic d.o.f. of the gravitational field. A Helmoltz-like equation is considered for the case of interactions that do not depend on the internal time and the corresponding Green's kernel is obtained exactly.The possibility of linking this approach to fundamental theories of Quantum Gravity is investigated.