Wavepacket evolution in unimodular quantum cosmology

TL;DR

This paper explores wavepacket evolution in unimodular quantum cosmology, deriving a Schrödinger-like equation, finding solutions for a flat universe with a massless scalar, and showing potential singularity resolution.

Contribution

It introduces a Schrödinger-like framework for unimodular quantum cosmology and provides explicit wavepacket solutions that can extend beyond classical singularities.

Findings

Wavepacket solutions exhibit unitary evolution.

Expectation values follow classical trajectories.

Solutions can be extended beyond the classical singularity.

Abstract

The unimodular theory of gravity admits a canonical quantization of minisuperspace models without the problem of time. We derive instead a kind of Schr\"odinger equation. We have found unitarily evolving wave packet solutions for the special case of a massless scalar field and a spatially flat Friedmann universe. We show that the longterm behaviour of the expectation values of the canonical quantities corresponds to the evolution of the classical variables. The solutions provided in an explicit example can be continued beyond the singularity at t=0, passing a finite minimal extension of the universe.