How to use Unimodular Quantum Cosmology for the Prediction of a late-time Classical Universe?

TL;DR

This paper explores how unimodular quantum cosmology can predict the emergence of a classical universe at late times by analyzing wavepacket evolution and expectation values in a simplified cosmological model.

Contribution

It provides an Ehrenfest theorem for unimodular quantum cosmology and investigates conditions under which quantum models yield classical universe behavior.

Findings

Classical and quantum behaviors coincide asymptotically for massless scalar fields.

Uncertainties analysis identifies models that lead to classical universe emergence.

Wavepacket solutions evolve according to a Schrödinger-like equation in unimodular quantum cosmology.

Abstract

Unimodular quantum cosmology admits wavepacket solutions that evolve according to a kind of Schr\"odinger equation. Though this theory is equivalent to general relativity on the classical level, its canonical structure is different and the problem of time does not occur. We present an Ehrenfest theorem for the long term evolution of the expectation value of the scale factor for a spatially flat Friedmann universe with a scalar field. We find that the classical and the quantum behaviour in the asymptotic future coincide for the special case of a massless scalar field. We examine the general behaviour of uncertainties in order to single out models that can lead to a classical universe.