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) | Viewed by 20550

Special Issue Editors

Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, EE-50411 Tartu, Estonia
Interests: theories of gravity; cosmology
Special Issues, Collections and Topics in MDPI journals
1. Institute of Space Sciences and Astronomy, University of Malta, Msida, Malta
2. Department of Physics, University of Malta, Msida, Malta
Interests: Cosmology; Modified Gravity; Large-Scale Structure
Special Issues, Collections and Topics in MDPI journals

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

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Keywords

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

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Published Papers (11 papers)

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Editorial

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3 pages, 170 KiB  
Editorial
Teleparallel Gravity: Foundations and Observational Constraints—Editorial
by Sebastian Bahamonde and Jackson Levi Said
Universe 2021, 7(8), 269; https://doi.org/10.3390/universe7080269 - 27 Jul 2021
Cited by 5 | Viewed by 1314
Abstract
Einstein’s formulation of general relativity as a theory based on the geometry of curvature was a necessity due to Riemannian geometry being the only fully developed framework at the time [...] Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

Research

Jump to: Editorial

24 pages, 442 KiB  
Article
Gravitationally Induced Particle Production through a Nonminimal Torsion–Matter Coupling
by Tiberiu Harko, Francisco S. N. Lobo and Emmanuel N. Saridakis
Universe 2021, 7(7), 227; https://doi.org/10.3390/universe7070227 - 05 Jul 2021
Cited by 17 | Viewed by 1542
Abstract
We investigate the possibility of gravitationally generated particle production via the mechanism of nonminimal torsion–matter coupling. An intriguing feature of this theory is that the divergence of the matter energy–momentum tensor does not vanish identically. We explore the physical and cosmological implications of [...] Read more.
We investigate the possibility of gravitationally generated particle production via the mechanism of nonminimal torsion–matter coupling. An intriguing feature of this theory is that the divergence of the matter energy–momentum tensor does not vanish identically. We explore the physical and cosmological implications of the nonconservation of the energy–momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard ΛCDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy–momentum tensor. We consider specific models, and we show that cosmology with a torsion–matter coupling can almost perfectly reproduce the ΛCDM scenario, while it additionally gives rise to particle creation rates, creation pressures, and entropy generation through gravitational matter production in both low and high redshift limits. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
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21 pages, 1809 KiB  
Article
Global Portraits of Nonminimal Teleparallel Inflation
by Laur Järv and Joosep Lember
Universe 2021, 7(6), 179; https://doi.org/10.3390/universe7060179 - 03 Jun 2021
Cited by 12 | Viewed by 1548
Abstract
We construct global phase portraits of inflationary dynamics in teleparallel gravity models with a scalar field nonminimally coupled to torsion scalar. The adopted set of variables can clearly distinguish between different asymptotic states as fixed points, including the kinetic and inflationary regimes. The [...] Read more.
We construct global phase portraits of inflationary dynamics in teleparallel gravity models with a scalar field nonminimally coupled to torsion scalar. The adopted set of variables can clearly distinguish between different asymptotic states as fixed points, including the kinetic and inflationary regimes. The key role in the description of inflation is played by the heteroclinic orbits that run from the asymptotic saddle points to the late time attractor point and are approximated by nonminimal slow roll conditions. To seek the asymptotic fixed points, we outline a heuristic method in terms of the “effective potential” and “effective mass”, which can be applied for any nonminimally coupled theories. As particular examples, we study positive quadratic nonminimal couplings with quadratic and quartic potentials and note how the portraits differ qualitatively from the known scalar-curvature counterparts. For quadratic models, inflation can only occur at small nonminimal coupling to torsion, as for larger coupling, the asymptotic de Sitter saddle point disappears from the physical phase space. Teleparallel models with quartic potentials are not viable for inflation at all, since for small nonminimal coupling, the asymptotic saddle point exhibits weaker than exponential expansion, and for larger coupling, it also disappears. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
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19 pages, 394 KiB  
Article
Static Spherically Symmetric Black Holes in Weak f(T)-Gravity
by Christian Pfeifer and Sebastian Schuster
Universe 2021, 7(5), 153; https://doi.org/10.3390/universe7050153 - 17 May 2021
Cited by 29 | Viewed by 1846
Abstract
With the advent of gravitational wave astronomy and first pictures of the “shadow” of the central black hole of our milky way, theoretical analyses of black holes (and compact objects mimicking them sufficiently closely) have become more important than ever. The near future [...] Read more.
With the advent of gravitational wave astronomy and first pictures of the “shadow” of the central black hole of our milky way, theoretical analyses of black holes (and compact objects mimicking them sufficiently closely) have become more important than ever. The near future promises more and more detailed information about the observable black holes and black hole candidates. This information could lead to important advances on constraints on or evidence for modifications of general relativity. More precisely, we are studying the influence of weak teleparallel perturbations on general relativistic vacuum spacetime geometries in spherical symmetry. We find the most general family of spherically symmetric, static vacuum solutions of the theory, which are candidates for describing teleparallel black holes which emerge as perturbations to the Schwarzschild black hole. We compare our findings to results on black hole or static, spherically symmetric solutions in teleparallel gravity discussed in the literature, by comparing the predictions for classical observables such as the photon sphere, the perihelion shift, the light deflection, and the Shapiro delay. On the basis of these observables, we demonstrate that among the solutions we found, there exist spacetime geometries that lead to much weaker bounds on teleparallel gravity than those found earlier. Finally, we move on to a discussion of how the teleparallel perturbations influence the Hawking evaporation in these spacetimes. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
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13 pages, 279 KiB  
Article
Minisuperspace Quantization of f(T, B) Cosmology
by Andronikos Paliathanasis
Universe 2021, 7(5), 150; https://doi.org/10.3390/universe7050150 - 16 May 2021
Cited by 11 | Viewed by 1593
Abstract
We discuss the quantization in the minisuperspace for the generalized fourth-order teleparallel cosmological theory known as fT, B. Specifically we focus on the case where the theory is linear on the torsion scalar, in that consideration we are able [...] Read more.
We discuss the quantization in the minisuperspace for the generalized fourth-order teleparallel cosmological theory known as fT, B. Specifically we focus on the case where the theory is linear on the torsion scalar, in that consideration we are able to write the cosmological field equations with the use of a scalar field different from the scalar tensor theories, but with the same dynamical constraints as that of scalar tensor theories. We use the minisuperspace description to write for the first time the Wheeler-DeWitt equation. With the use of the theory of similarity transformations we are able to find exact solutions for the Wheeler-DeWitt equations as also to investigate the classical and semiclassical limit in the de Broglie -Bohm representation of quantum mechanics. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
17 pages, 303 KiB  
Article
Renormalizability of Alternative Theories of Gravity: Differences between Power Counting and Entropy Argument
by Francesco Bajardi, Francesco Bascone and Salvatore Capozziello
Universe 2021, 7(5), 148; https://doi.org/10.3390/universe7050148 - 14 May 2021
Cited by 10 | Viewed by 1607
Abstract
It is well known that General Relativity cannot be considered under the standard of a perturbatively renormalizable quantum field theory, but asymptotic safety is taken into account as a possibility for the formulation of gravity as a non-perturbative renormalizable theory. Recently, the entropy [...] Read more.
It is well known that General Relativity cannot be considered under the standard of a perturbatively renormalizable quantum field theory, but asymptotic safety is taken into account as a possibility for the formulation of gravity as a non-perturbative renormalizable theory. Recently, the entropy argument has however stepped into the discussion claiming for a “no-go” to the asymptotic safety argument. In this paper, we present simple counter-examples, considering alternative theories of gravity, to the entropy argument as further indications, among others, on the possible flows in the assumptions on which the latter is based. We considered different theories, namely curvature-based extensions of General Relativity as f(R), f(G), extensions of teleparallel gravity as f(T), and Horava–Lifshitz gravity, working out the explicit spherically symmetric solutions in order to make a comparison between power counting and the entropy argument. Even in these cases, inconsistencies were found. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
16 pages, 301 KiB  
Article
Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories
by Jose Beltrán Jiménez and Tomi S. Koivisto
Universe 2021, 7(5), 143; https://doi.org/10.3390/universe7050143 - 12 May 2021
Cited by 22 | Viewed by 1254
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)
11 pages, 275 KiB  
Communication
Approaches to Spherically Symmetric Solutions in f(T) Gravity
by Alexey Golovnev and María-José Guzmán
Universe 2021, 7(5), 121; https://doi.org/10.3390/universe7050121 - 29 Apr 2021
Cited by 19 | Viewed by 1191
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 [...] Read more.
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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25 pages, 348 KiB  
Article
Variational Principles in Teleparallel Gravity Theories
by Manuel Hohmann
Universe 2021, 7(5), 114; https://doi.org/10.3390/universe7050114 - 21 Apr 2021
Cited by 37 | Viewed by 2689
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)
18 pages, 466 KiB  
Article
Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole
by José Wadih Maluf, Sérgio Ulhoa, Fernando Lessa Carneiro and Karlúcio H. C. Castello-Branco
Universe 2021, 7(4), 100; https://doi.org/10.3390/universe7040100 - 14 Apr 2021
Cited by 4 | Viewed by 1740
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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13 pages, 259 KiB  
Article
An Improved Framework for Quantum Gravity
by José G. Pereira and Diego F. López
Universe 2020, 6(12), 243; https://doi.org/10.3390/universe6120243 - 16 Dec 2020
Cited by 3 | Viewed by 1987
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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