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.
Highlights
The canonical quantization of general relativity leads to the so-called problem of time
If instead a perfect fluid matter model is chosen, the solutions for a massless scalar field can be shown to be equivalent to the solutions for the special case of stiff matter
An approximate classical behaviour far away from the singularity was predicted for the case of exotic matter in [5]
Summary
The canonical quantization of general relativity leads to the so-called problem of time (see [1] and references therein). In most non-perturbative approaches of quantum gravity time has disappeared from the theory and is seen as an artifact of the classical limit. In contrast to this we will discuss here the quantization of a minisuperspace model in the framework of unimodular gravity. This theory is practically equivalent to general relativity at the classical level, but since it has a different canonical structure time does not disappear from the quantum theory [2]. In this article we consider the quantization of spatially flat universe with a massless scalar field. Based on an example we investigate the time evolution of characteristic expectation values and compare it to the classical dynamics
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
