WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings

Understand

In this review, we analyse different aspects concerning the possibility to separate a gravity-matter system into a part which lives close to a quasi-classical state and a "small" quantum subset.

• The considered approaches are all relying on a WKB expansion of the dynamics by an order parameter and the natural arena consists of the Bianchi universe minisuperspace.
• We first discuss how, limiting the WKB expansion to the first order of approximation, it is possible to recover for the quantum subsystem a Schr\"odinger equation as written on the classical gravitational background.
• We give some applications for the quantum subsystem in the "corner" configuration of the Bianchi IX model, identifying the quantum variable in the small one of the two anisotropy degrees of freedom.