Special Issue "Teleparallel Gravity: Foundations and Observational Constraints"

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Gravitation".

Deadline for manuscript submissions: closed (31 March 2021).

Special Issue Editors

Dr. Sebastian Bahamonde
E-Mail Website
Guest Editor
Laboratory of Theoretical Physics, Institute of Physics, University of Tartu
Interests: Modified gravity; Cosmology; Teleparallel gravity
Dr. Jackson Levi Said
E-Mail
Guest Editor
Institute of Space Sciences and Astronomy, University of Malta, Malta
Department of Physics, University of Malta, Malta
Interests: Cosmology; Modified Gravity; Large-Scale Structure

Special Issue Information

Dear Colleagues,

General relativity is a very successful theory that shows great agreement with observations. However, the theory faces some theoretical and observational challenges, such as the issues surrounding dark energy or dark matter as well as cosmological tensions in recent large-scale structure measurements. In order to try to tackle these issues, several types of modified theories of gravity have been proposed. One interesting route is to modify the geometrical nature of gravity. This is done in the so-called “teleparallel theories of gravity”, where the manifold is assumed to be flat (zero curvature) but could contain torsion and/or non-metricity. It turns out that one can write down theories having the same field equations (and predictions) to general relativity using two alternative routes: from torsion (torsional teleparallel) or from non-metricity (symmetric teleparallel). Following this, one could extend these theories to obtain modified theories different from the standard GR-based theories. 

This Special issue is devoted to all aspects of teleparallel theories of gravity, containing torsion and/or non-metricity. The main aim would be to focus on their theoretical foundations and, also, on possible observational constraints that one can set from cosmology and astrophysics.  

Dr. Sebastian Bahamonde
Dr. Jackson Levi Said
Guest Editors

Manuscript Submission Information

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Keywords

  • Modified Gravity
  • Teleparallel Gravity
  • Symmetric Teleparallel Gravity
  • Observational Constraints
  • Cosmology
  • Astrophysics
  • Gravitational Radiation

Published Papers (5 papers)

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Research

Open AccessArticle
Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories
by and
Universe 2021, 7(5), 143; https://doi.org/10.3390/universe7050143 (registering DOI) - 12 May 2021
Viewed by 99
Abstract
In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the [...] Read more.
In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
Open AccessCommunication
Approaches to Spherically Symmetric Solutions in f(T) Gravity
Universe 2021, 7(5), 121; https://doi.org/10.3390/universe7050121 - 29 Apr 2021
Viewed by 141
Abstract
We study properties of static spherically symmetric solutions in f(T) gravity. Based on our previous work on generalizing Bianchi identities for this kind of theory, we show how this search for solutions can be reduced to the study of two relatively simple equations. One of them does not depend on the function f and therefore describes the properties of such solutions in any f(T) theory. Another equation is the radial one and, if a possible solution is chosen, it allows the discovery of which function f is suitable for it. We use these equations to find exact and perturbative solutions for arbitrary and specific choices of f. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
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Open AccessArticle
Variational Principles in Teleparallel Gravity Theories
Universe 2021, 7(5), 114; https://doi.org/10.3390/universe7050114 - 21 Apr 2021
Cited by 1 | Viewed by 182
Abstract
We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that, in addition to the tetrad or metric, they employ a flat [...] Read more.
We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that, in addition to the tetrad or metric, they employ a flat connection as additional field variable, but dthey iffer by the presence of absence of torsion and nonmetricity for this independent connection. Besides the different underlying geometric formulation using a tetrad or metric as fundamental field variable, one has different choices to introduce the conditions of vanishing curvature, torsion, and nonmetricity, either by imposing them a priori and correspondingly restricting the variation of the action when the field equations are derived, or by using Lagrange multipliers. Special care must be taken, since these conditions form non-holonomic constraints. Here, we explicitly show that all of the aforementioned approaches are equivalent, and that the same set of field equations is obtained, independently of the choice of the geometric formulation and variation procedure. We further discuss the consequences arising from the diffeomorphism invariance of the gravitational action, and show how they establish relations between the gravitational field equations. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
Open AccessArticle
Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole
Universe 2021, 7(4), 100; https://doi.org/10.3390/universe7040100 - 14 Apr 2021
Viewed by 232
Abstract
We calculate the gravitational energy spectrum of the perturbations of a Schwarzschild black hole described by quasinormal modes, in the framework of the teleparallel equivalent of general relativity (TEGR). We obtain a general formula for the gravitational energy enclosed by a large surface [...] Read more.
We calculate the gravitational energy spectrum of the perturbations of a Schwarzschild black hole described by quasinormal modes, in the framework of the teleparallel equivalent of general relativity (TEGR). We obtain a general formula for the gravitational energy enclosed by a large surface of constant radius r, in the region m<<r<<, where m is the mass of the black hole. Considering the usual asymptotic expression for the perturbed metric components, we arrive at finite values for the energy spectrum. The perturbed energy depends on the two integers n and l that describe the quasinormal modes. In this sense, the energy perturbations are discretized. We also obtain a simple expression for the decrease of the flux of gravitational radiation of the perturbations. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
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Open AccessArticle
An Improved Framework for Quantum Gravity
Universe 2020, 6(12), 243; https://doi.org/10.3390/universe6120243 - 16 Dec 2020
Viewed by 558
Abstract
General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field’s quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces apart. The second problem is its incompatibility with quantum mechanics, a [...] Read more.
General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field’s quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces apart. The second problem is its incompatibility with quantum mechanics, a problem inherited from the more fundamental conflict of special relativity with quantum mechanics. A procedure to overcome these difficulties is outlined, which amounts to replacing general relativity with its teleparallel equivalent and the Poincaré-invariant special relativity with the de Sitter-invariant special relativity. Those replacements give rise to the de Sitter-modified teleparallel gravity, which does not have the two mentioned problems. It can thus be considered an improved alternative approach to quantum gravity. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
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