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Universe
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Selected Papers from Teleparallel Universes in Salamanca
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Selected Papers from Teleparallel Universes in Salamanca

A special issue of Universe (ISSN 2218-1997).

Deadline for manuscript submissions: closed (30 April 2019) | Viewed by 24507

Special Issue Editors

Prof. Dr. Tomi Koivisto

E-Mail Website
Guest Editor
Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
Interests: cosmological models; theory of gravity; foundations
Dr. Jose Beltran Jimenez

E-Mail Website
Guest Editor
Departamento de Fısica Fundamental, Universidad de Salamanca, E-37008 Salamanca, Spain
Interests: cosmology; gravity
Dr. Lavinia Heisenberg

E-Mail Website
Guest Editor
Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich, Switzerland
Interests: cosmology; gravity
Dr. Alexey Golovnev

E-Mail Website
Guest Editor
Faculty of Physics, St. Petersburg State University, Ulyanovskaya ul., d. 1, Saint Petersburg 198504, Russia
Interests: cosmology; gravity

Special Issue Information

Dear Colleagues,

Gravity is commonly understood as a geometric phenomenon. This understanding goes back to Einstein's formulation of the General Theory of Relativity, which attributes gravity to the curvature of spacetime. The great insight underlying this theory was the unification of gravity and inertia, which allows the geometric description of the gravitational interaction as spacetime curvature anticipated by both Riemann and Clifford.

However, equivalent descriptions are known in terms of torsion and non-metricity. Due to the flatness of the connection in these alternative formulations, they are called teleparallel theories. It is timely to explore gravity in this alternative framework, as the conventional version of General Relativity, despite its great success in describing numerous phenomena, is being challenged by many observational and conceptual problems. The most prominent observational issues are cosmological: the Universe, as described by General Relativity, seems to be filled with invisible matter and unexplained energy whose density remains nearly constant in the expanding space. The conceptual issues are mostly related to quantum theory: notoriously, gravity has not been quantised, and foundational questions regarding the nature of space and time remain without conclusive answers.

The analysis of General Relativity in generalised geometry was begun by Hermann Weyl a century ago in 1918, and it eventually lead to the development of the gauge theories comprising the modern standard model of particle physics. Nevertheless, the theory of gravity remains to be unified in this context. Like the other fundamental interactions of nature, we believe that gravitation also can be described in terms of a gauge theory, and, in particular, teleparallel formulations have been considered as gauge theories of the group of translations. Elie Cartan had laid important mathematical foundations by introducing the concepts of moving frames and torsion. One of the well-known frameworks wherein teleparallelism may be naturally embedded is metric affine gauge theory, featuring both Weyl’s non-metricity and Cartan’s torsion.

This Special Issue of Universe reports proceedings of the workshop Teleparallel Universes in Salamanca (26-28 November 2018). The research and review articles will reflect recent developments at the frontiers of teleparallel theory. Different covariant formulations are presented, and the theory is approached from the premetric perspective and in terms of Cartan geometry. The important and open issue of the degrees of freedom in generalised theories is discussed in several papers using the Hamiltonian formalism. The phenomenology of teleparallel theories is considered in the framework of black holes and cosmology. A reappraisal of cosmology based on teleparallel gravity could provide a new way to look at the Universe, unveiling perspectives that may resolve the cosmological constant problem, the nature of dark energy and dark matter, and the genesis of the Universe in the inflationary or alternative scenarios.

Prof. Dr. Tomi Koivisto
Dr. Jose Beltran Jimenez
Dr. Lavinia Heisenberg
Dr. Alexey Golovnev
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • teleparallel equivalent of general relativity
  • symmetric teleparallel equivalent of general relativity
  • gauge theories of gravitation
  • cosmology
  • dark energy and modified gravity
  • black holes in alternative theories of gravity
  • Cartan geometry
  • premetric gravity
  • metric affine gauge theory

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Published Papers (9 papers)

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Research

6 pages, 254 KiB  
Communication
The General Linear Cartan Khronon
by Tomi Koivisto, Manuel Hohmann and Tom Złośnik
Universe 2019, 5(7), 168; https://doi.org/10.3390/universe5070168 - 8 Jul 2019
Cited by 23 | Viewed by 2356
Abstract
A Cartan geometry of the General Linear symmetry is formulated by dividing out the displacements from the group. The resulting action is quadratic in curvature, polynomial in all the (minimal) variables, and describes an observer space that—in the symmetry-broken phase—reproduces the predictions of [...] Read more.
A Cartan geometry of the General Linear symmetry is formulated by dividing out the displacements from the group. The resulting action is quadratic in curvature, polynomial in all the (minimal) variables, and describes an observer space that—in the symmetry-broken phase—reproduces the predictions of General Relativity in the presence of dark matter. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
10 pages, 224 KiB  
Article
Disformal Transformations in Scalar–Torsion Gravity
by Manuel Hohmann
Universe 2019, 5(7), 167; https://doi.org/10.3390/universe5070167 - 7 Jul 2019
Cited by 20 | Viewed by 2324
Abstract
We study disformal transformations in the context of scalar extensions to teleparallel gravity, in which the gravitational interaction is mediated by the torsion of a flat, metric compatible connection. We find a generic class of scalar–torsion actions which is invariant under disformal transformations, [...] Read more.
We study disformal transformations in the context of scalar extensions to teleparallel gravity, in which the gravitational interaction is mediated by the torsion of a flat, metric compatible connection. We find a generic class of scalar–torsion actions which is invariant under disformal transformations, and which possesses different invariant subclasses. For the most simple of these subclasses we explicitly derive all terms that may appear in the action. We propose to study actions from this class as possible teleparallel analogues of healthy beyond Horndeski theories. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
15 pages, 293 KiB  
Article
Reflections on the Covariance of Modified Teleparallel Theories of Gravity
by Cecilia Bejarano, Rafael Ferraro, Franco Fiorini and María José Guzmán
Universe 2019, 5(6), 158; https://doi.org/10.3390/universe5060158 - 25 Jun 2019
Cited by 37 | Viewed by 2675
Abstract
We review the current status of the Lorentz covariance in teleparallel and modified teleparallel theories of gravity, and discuss the controversial features of the different approaches. We also revisit the issue of the remnant Lorentz gauge symmetries in f ( T ) gravity. [...] Read more.
We review the current status of the Lorentz covariance in teleparallel and modified teleparallel theories of gravity, and discuss the controversial features of the different approaches. We also revisit the issue of the remnant Lorentz gauge symmetries in f ( T ) gravity. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
7 pages, 240 KiB  
Communication
On the Gauge Fixing in the Hamiltonian Analysis of General Teleparallel Theories
by Daniel Blixt, Manuel Hohmann and Christian Pfeifer
Universe 2019, 5(6), 143; https://doi.org/10.3390/universe5060143 - 10 Jun 2019
Cited by 38 | Viewed by 2313
Abstract
The covariant formulation of teleparallel gravity theories must include the spin connection, which has 6 degrees of freedom. One can, however, always choose a gauge such that the spin connection is put to zero. In principle this gauge may affect counting of degrees [...] Read more.
The covariant formulation of teleparallel gravity theories must include the spin connection, which has 6 degrees of freedom. One can, however, always choose a gauge such that the spin connection is put to zero. In principle this gauge may affect counting of degrees of freedom in the Hamiltonian analysis. We show for general teleparallel theories of gravity, that fixing the gauge such that the spin connection vanishes in fact does not affect the counting of degrees of freedom. This manifests in the fact that the momenta of the Lorentz transformations which generate the spin connection are fully determined by the momenta of the tetrads. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
13 pages, 338 KiB  
Article
Flat Connection for Rotating Vacuum Spacetimes in Extended Teleparallel Gravity Theories
by Laur Järv, Manuel Hohmann, Martin Krššák and Christian Pfeifer
Universe 2019, 5(6), 142; https://doi.org/10.3390/universe5060142 - 10 Jun 2019
Cited by 22 | Viewed by 2469
Abstract
Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi–Civita connection. In extended teleparallel theories, for instance in f ( T ) or scalar-torsion gravity, the connection must obey its antisymmetric [...] Read more.
Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi–Civita connection. In extended teleparallel theories, for instance in f ( T ) or scalar-torsion gravity, the connection must obey its antisymmetric field equations. Thus far, only a few analytic solutions were known. In this note, we solve the f ( T , ϕ ) gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformation, we present the solution also in Boyer–Lindquist coordinates, often used to study rotating solutions in general relativity. The result hints for the existence of another branch of rotating solutions besides the Kerr family in extended teleparallel gravities. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
8 pages, 736 KiB  
Communication
Gauge Structure of Teleparallel Gravity
by José G. Pereira and Yuri N. Obukhov
Universe 2019, 5(6), 139; https://doi.org/10.3390/universe5060139 - 5 Jun 2019
Cited by 54 | Viewed by 2669
Abstract
During the conference Teleparallel Universes in Salamanca, we became aware of a recent paper [M. Fontanini, E. Huguet, and M. Le Delliou, Phys. Rev. D 2019, 99, 064006] in which some criticisms on the interpretation of teleparallel gravity as a gauge [...] Read more.
During the conference Teleparallel Universes in Salamanca, we became aware of a recent paper [M. Fontanini, E. Huguet, and M. Le Delliou, Phys. Rev. D 2019, 99, 064006] in which some criticisms on the interpretation of teleparallel gravity as a gauge theory for the translation group were put forward. This triggered a discussion about the arguments on which those criticisms were based, whose output is described in the present paper. The main conclusion is that to a great extent, those arguments are incorrect, and lack mathematical and physical support. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
13 pages, 295 KiB  
Article
Exact Solutions in Poincaré Gauge Gravity Theory
by Yuri N. Obukhov
Universe 2019, 5(5), 127; https://doi.org/10.3390/universe5050127 - 24 May 2019
Cited by 24 | Viewed by 2611
Abstract
In the framework of the gauge theory based on the Poincaré symmetry group, the gravitational field is described in terms of the coframe and the local Lorentz connection. Considered as gauge field potentials, they give rise to the corresponding field strength which are [...] Read more.
In the framework of the gauge theory based on the Poincaré symmetry group, the gravitational field is described in terms of the coframe and the local Lorentz connection. Considered as gauge field potentials, they give rise to the corresponding field strength which are naturally identified with the torsion and the curvature on the Riemann–Cartan spacetime. We study the class of quadratic Poincaré gauge gravity models with the most general Yang–Mills type Lagrangian which contains all possible parity-even and parity-odd invariants built from the torsion and the curvature. Exact vacuum solutions of the gravitational field equations are constructed as a certain deformation of de Sitter geometry. They are black holes with nontrivial torsion. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
34 pages, 459 KiB  
Article
Scale Transformations in Metric-Affine Geometry
by Damianos Iosifidis and Tomi Koivisto
Universe 2019, 5(3), 82; https://doi.org/10.3390/universe5030082 - 15 Mar 2019
Cited by 80 | Viewed by 3564
Abstract
This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformation of the connection, a rescaling of the orthonormal frame, [...] Read more.
This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformation of the connection, a rescaling of the orthonormal frame, and a combination of the two. The most general second order quadratic metric-affine action, including the parity-violating terms, is constructed in each of the three cases. The results can be straightforwardly generalised by including higher derivatives, and implemented in the general metric-affine, teleparallel, and symmetric teleparallel geometries. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
9 pages, 309 KiB  
Article
The Spectrum of Teleparallel Gravity
by Tomi Koivisto and Georgios Tsimperis
Universe 2019, 5(3), 80; https://doi.org/10.3390/universe5030080 - 14 Mar 2019
Cited by 42 | Viewed by 2627
Abstract
The observer’s frame is the more elementary description of the gravitational field than the metric. The most general covariant, even-parity quadratic form for the frame field in arbitrary dimension generalises the New General Relativity by nine functions of the d’Alembertian operator. The degrees [...] Read more.
The observer’s frame is the more elementary description of the gravitational field than the metric. The most general covariant, even-parity quadratic form for the frame field in arbitrary dimension generalises the New General Relativity by nine functions of the d’Alembertian operator. The degrees of freedom are clarified by a covariant derivation of the propagator. The consistent and viable models can incorporate an ultra-violet completion of the gravity theory, an additional polarisation of the gravitational wave, and the dynamics of a magnetic scalar potential. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
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