Teleparallel gravity: from theory to cosmology

Bahamonde, S., Dialektopoulos, K., Escamilla-Rivera, C., Farrugia, G., Gakis, V., Hendry, M. , Hohmann, M., Said, J., Mifsud, J. and Di Valentino, E. (2023) Teleparallel gravity: from theory to cosmology. Reports on Progress in Physics, 86(2), 026901. (doi: 10.1088/1361-6633/ac9cef)

Abstract

Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we give a comprehensive introduction to how teleparallel geometry is developed as a gauge theory of translations together with all the other properties of gauge field theory. We also related this form of geometry to the broader metric-affine approach to forming gravitational theories where we describe a systematic way of constructing consistent teleparallel theories that respect certain physical conditions such as local Lorentz invariance. We first use teleparallel gravity to formulate a teleparallel equivalent of general relativity which is dynamically equivalent to general relativity but which may have different behaviors for other scenarios, such as quantum gravity. After setting this foundation, we describe the plethora of modified teleparallel theories of gravity that have been proposed in the literature. We attempt to connect them together into general classes of covariant gravitational theories. Of particular interest, we highlight the recent proposal of a teleparallel analogue of Horndeski gravity which offers the possibility of reviving all of the regular Horndeski contributions. In the second part of the Review, we first survey works in teleparallel astrophysics literature where we focus on the open questions in this regime of physics. We then discuss the cosmological consequences for the various formulations of teleparallel gravity. We do this at background level by exploring works using various approaches ranging from dynamical systems to Noether symmetries, and more. Naturally, we then discuss perturbation theory, firstly by giving a concise approach in which this can be applied in teleparallel gravity theories and then apply it to a number of important theories in the literature. Finally, we examine works in observational and precision cosmology across the plethora of proposal theories. This is done using some of the latest observations and is used to tackle cosmological tensions which may be alleviated in teleparallel cosmology. We also introduce a number of recent works in the application of machine learning to gravity, we do this through deep learning and Gaussian processes, together with discussions about other approaches in the literature.

• Item Type: Articles
• Additional Information: SB and MH were supported by the Estonian Research Council grants PRG356 “Gauge Gravity" and by the European Regional Development Fund through the Center of Excellence TK133 “The Dark Side of the Universe". SB is also supported by JSPS Postdoctoral Fellowships for Research in Japan and KAKENHI Grant-in-Aid for Scientific Research No. JP21F21789. KFD acknowledges support by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “First Call for H.F.R.I. Research Projects to support Faculty members and Researchers and the procurement of high-cost research equipment grant” (Project Number: 2251). The work was also supported by Nazarbayev University Faculty Development Competitive Research Grant No. 11022021FD2926. CE-R acknowledges the Royal Astronomical Society as FRAS 10147 and DGAPA-PAPIIT-UNAM Project IA100220. JLS and JM would also like to acknowledge funding support from Cosmology@MALTA which is supported by the University of Malta. JLS would also like to acknowledge funding from “The Malta Council for Science and Technology” in project IPAS-2020-007. EDV acknowledges the support of the Addison-Wheeler Fellowship awarded by the Institute of Advanced Study at Durham University. This research was partially carried out using computational facilities procured through the European Regional Development Fund, Project No. ERDF-080 “A supercomputing laboratory for the University of Malta” and the “CosmoNag project” through Tochtli ICN-UNAM cluster.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Hendry, Professor Martin
• Authors: Bahamonde, S., Dialektopoulos, K., Escamilla-Rivera, C., Farrugia, G., Gakis, V., Hendry, M., Hohmann, M., Said, J., Mifsud, J., and Di Valentino, E.
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Research Centre: College of Science and Engineering > School of Physics and Astronomy > Institute for Gravitational Research
• Journal Name: Reports on Progress in Physics
• Publisher: IOP Publishing
• ISSN: 0034-4885
• ISSN (Online): 1361-6633
• Published Online: 24 October 2022
• Copyright Holders: Copyright © 2022 IOP Publishing Ltd
• First Published: First published in Reports on Progress in Physics 86(2): 026901
• Publisher Policy: Reproduced in accordance with the publisher copyright policy