WKB approach to the gravity-matter dynamics: a cosmological implementation

TL;DR

This paper introduces a novel WKB-based method for defining a relational time in quantum gravity-matter systems, ensuring unitary evolution and maintaining covariance, with applications to cosmology.

Contribution

It proposes a new quantization approach using the kinematical action as a clock, overcoming non-unitarity issues in previous models.

Findings

Quantum gravity corrections appear at the next order in WKB expansion.

The new method maintains covariance and classical limit.

Quantum matter evolution remains unitary with the proposed approach.

Abstract

The problem of time emerging in the canonical quantization procedure of gravity signals a necessity to properly define a relational time parameter. Previous approaches, which are here briefly discussed, make use of the dependence of the quantum system on semiclassical gravitational variables in order to define time. We show that such paths, despite the following studies, lead to a non-unitary evolution. We propose a different model for the quantization of the gravity-matter system, where the time parameter is defined via an additional term, i.e. the kinematical action, which acts as a clock for quantum matter. The procedure here used implements a Born-Oppenheimer-like separation of the system, which maintains covariance under the foliation of the gravitational background and keeps the correct classical limit of standard quantum field theory on a fixed background. It is shown with a WKB expansion that quantum gravity corrections to the matter dynamics arise at the next order of expansion, and such contributions are unitary, signalling a striking difference from previous proposals. Applications to a cosmological model are presented and the analogies of the kinematical term with an incoherent dust are briefly discussed.