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Bahamonde S, Dialektopoulos KF, Escamilla-Rivera C, Farrugia G, Gakis V, Hendry M, Hohmann M, Levi Said J, Mifsud J, Di Valentino E. Teleparallel gravity: from theory to cosmology. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:026901. [PMID: 36279849 DOI: 10.1088/1361-6633/ac9cef] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Accepted: 10/24/2022] [Indexed: 06/16/2023]
Abstract
Teleparallel gravity (TG) 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. This relates the 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 TG to formulate a teleparallel equivalent of general relativity (GR) which is dynamically equivalent to GR 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 TG. 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 TG 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.
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Affiliation(s)
- Sebastian Bahamonde
- Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
- Department of Physics, Tokyo Institute of Technology, 1-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
| | - Konstantinos F Dialektopoulos
- Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, People's Republic of China
- Laboratory of Physics, Faculty of Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
- Department of Physics, Nazarbayev University, 53 Kabanbay Batyr Avenue, 010000 Astana, Kazakhstan
| | - Celia Escamilla-Rivera
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior C.U., A.P. 70-543, México D.F. 04510, Mexico
| | - Gabriel Farrugia
- Institute of Space Sciences and Astronomy, University of Malta, Msida, Malta
- Department of Physics, University of Malta, Msida, Malta
| | - Viktor Gakis
- Institute of Space Sciences and Astronomy, University of Malta, Msida, Malta
- Department of Physics, University of Malta, Msida, Malta
- Department of Physics, National Technical University of Athens, Zografou Campus GR 157 73, Athens, Greece
| | - Martin Hendry
- SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
| | - Manuel Hohmann
- Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
| | - Jackson Levi Said
- Institute of Space Sciences and Astronomy, University of Malta, Msida, Malta
- Department of Physics, University of Malta, Msida, Malta
| | - Jurgen Mifsud
- Institute of Space Sciences and Astronomy, University of Malta, Msida, Malta
- Department of Physics, University of Malta, Msida, Malta
| | - Eleonora Di Valentino
- Institute for Particle Physics Phenomenology, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
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