Gielen, S. orcid.org/0000-0002-8653-5430 and Mickel, L. orcid.org/0000-0002-6749-8494 (2024) Reconstructing the metric in group field theory. Classical and Quantum Gravity, 41 (16). 165002. ISSN 0264-9381
Abstract
We study a group field theory (GFT) for quantum gravity coupled to four massless scalar fields, using these matter fields to define a (relational) coordinate system. We exploit symmetries of the GFT action, in particular under shifts in the values of the scalar fields, to derive a set of classically conserved currents, and show that the same conservation laws hold exactly at the quantum level regardless of the choice of state. We propose a natural interpretation of the conserved currents which implies that the matter fields always satisfy the Klein–Gordon equation in GFT. We then observe that in our matter reference frame, the same conserved currents can be used to extract all components of an effective GFT spacetime metric. Finally, we apply this construction to the simple example of a spatially flat homogeneous and isotropic Universe, where we derive an effective Friedmann equation directly from this metric. The Friedmann equation displays a bounce and a late-time limit equivalent to general relativity with a single scalar field. Our proposal goes substantially beyond the GFT literature in which only specific geometric quantities such as the total volume or volume perturbations could be defined, opening up the possibility to study more general geometries as emerging from GFT.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Author(s). Published by IOP Publishing Ltd. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
Keywords: | quantum gravity; group field theory; relational dynamics |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 23 Jul 2024 11:06 |
Last Modified: | 23 Jul 2024 11:06 |
Status: | Published |
Publisher: | IOP Publishing |
Refereed: | Yes |
Identification Number: | 10.1088/1361-6382/ad5bb6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:215018 |
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