[2106.13793] Teleparallel Gravity: From Theory to Cosmology

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General Relativity and Quantum Cosmology

arXiv:2106.13793 (gr-qc)

[Submitted on 25 Jun 2021 (v1), last revised 21 Feb 2023 (this version, v4)]

Title:Teleparallel Gravity: From Theory to Cosmology

Authors:Sebastian Bahamonde, Konstantinos F. Dialektopoulos, Celia Escamilla-Rivera, Gabriel Farrugia, Viktor Gakis, Martin Hendry, Manuel Hohmann, Jackson Levi Said, Jurgen Mifsud, Eleonora Di Valentino<br>View a PDF of the paper titled Teleparallel Gravity: From Theory to Cosmology, by Sebastian Bahamonde and 8 other authors

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Abstract:Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we relate 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. 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.

Comments:<br>391 pages, 55 figures

Subjects:

General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO)

Cite as:<br>arXiv:2106.13793 [gr-qc]

(or<br>arXiv:2106.13793v4 [gr-qc] for this version)

https://doi.org/10.48550/arXiv.2106.13793

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arXiv-issued DOI via DataCite

Journal reference:<br>Rep. Prog. Phys. 86 026901 (2023)

Related DOI:

https://doi.org/10.1088/1361-6633/ac9cef

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DOI(s) linking to related resources

Submission history<br>From: Jackson Levi Said [view email]<br>[v1]<br>Fri, 25 Jun 2021 17:45:41 UTC (9,607 KB)

[v2]<br>Mon, 2 Aug 2021 14:17:34 UTC (19,516 KB)

[v3]<br>Thu, 9 Sep 2021 12:47:09 UTC (19,226 KB)

[v4]<br>Tue, 21 Feb 2023 10:54:43 UTC (10,256 KB)

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