New Results in One-Loop Quantum Cosmology

TL;DR

This paper investigates the one-loop semiclassical approximation in quantum cosmology, focusing on Euclidean quantum gravity with boundary conditions, gauge effects, and implications for supergravity's finiteness.

Contribution

It provides new insights into gauge and ghost mode effects, boundary condition impacts, and the limitations of one-loop finiteness in simple supergravity.

Findings

One-loop divergence matches Schwinger-DeWitt results after gauge and ghost mode considerations.

Boundary conditions involving tangential derivatives affect heat-kernel asymptotics.

Boundary effects prevent one-loop finiteness in simple supergravity with a single boundary.

Abstract

A crucial problem in quantum cosmology is a careful analysis of the one-loop semiclassical approximation for the wave function of the universe, after an appropriate choice of mixed boundary conditions. The results for Euclidean quantum gravity in four dimensions are here presented, when linear covariant gauges are implemented by means of the Faddeev-Popov formalism. On using zeta-function regularization and a mode-by-mode analysis, one finds a result for the one-loop divergence which agrees with the Schwinger-DeWitt method only after taking into account the non-trivial effect of gauge and ghost modes. For the gravitational field, however, the geometric form of heat-kernel asymptotics with boundary conditions involving tangential derivatives of metric perturbations is still unknown. Moreover, boundary effects are found to be responsible for the lack of one-loop finiteness of simple supergravity, when only one bounding three-surface occurs. This work raises deep interpretative issues about the admissible backgrounds and about quantization techniques in quantum cosmology.