Quantum Gravity and Turning Points in the Semiclassical Approximation

TL;DR

This paper investigates the impact of turning points in the gravitational variables on the semiclassical approximation in quantum gravity, showing that the matter wavefunction recovers after evolving past the turning point and analyzing corrections.

Contribution

It provides a detailed analysis of turning points in quantum gravity's semiclassical approximation and demonstrates recovery of the matter wavefunction, including leading backreaction corrections.

Findings

Matter wavefunction recovers after turning points in gravity variables.

Leading backreaction corrections are computed in simple models.

Turning points can occur in the gravitational sector in dilaton gravity.

Abstract

The wavefunctional in quantum gravity gives an amplitude for 3-geometries and matter fields. The four-space is usually recovered in a semiclassical approximation where the gravity variables are taken to oscillate rapidly compared to matter variables; this recovers the Schrodinger evolution for the matter. We examine turning points in the gravity variables where this approximation appears to be troublesome. We investigate the effect of such a turning point on the matter wavefunction, in simple quantum mechanical models and in a closed minisuperspace cosmology. We find that after evolving sufficiently far from the turning point the matter wavefunction recovers to a form close to that predicted by the semiclassical approximation, and we compute the leading correction (from `backreaction') in a simple model. We also show how turning points can appear in the gravitational sector in dilaton gravity. We give some remarks on the behavior of the wavefunctional in the vicinity of turning points in the context of dilaton gravity black holes.