Related papers: Geometry of teleparallel theories
The notion of a parallelizable distribution has been introduced and investigated. A non-integrable parallelizable distribution carries a natural sub-Riemannian structure. The geometry of this structure has been studied from the bi-viewpoint…
The status of the equivalence principle in modified symmetric teleparallel gravity is examined. In this theory, minimum length geodesics are distinct from autoparallel geodesics, that is, the ``shortest'' paths are not the ``straightest''…
Although the autoparallel curves and the geodesics coincide in the Riemannian geometry in which only the curvature is nonzero among the nonmetricity, the torsion and the curvature, they define different curves in the non-Riemannian ones. We…
We derive the most general homogeneous and isotropic teleparallel geometries, defined by a metric and a flat, affine connection. We find that there are five branches of connection solutions, which are connected via several limits, and can…
Local Lorentz transformations play an important role in teleparallel gravity theories, in which a tetrad is conventionally employed as a fundamental field variable describing the gravitational field. It is commonly understood that…
Some conceptual issues concerning $f(T)$ theories --a family of modified gravity theories based on absolute parallelism-- are analyzed. Due to the lack of local Lorentz invariance, the autoparallel frames satisfying the field equations are…
Recently, an extension of teleparallelism to a Weyl geometry which allows us to easily establish conformal invariance and "geometrize" electromagnetism has been presented. In this paper, I extend a result which concerns the existence of the…
The geometry of parallelizable manifolds (i.e., teleparallelism) is summarized in the language of local frame fields. Some problems in continuum mechanics that relate to the couple-stresses that are produced in the bending and twisting of…
This thesis studies modified theories of gravity from a geometric viewpoint. We review the motivations for considering alternatives to General Relativity and cover the mathematical foundations of gravitational theories in Riemannian and…
Teleparallel gravity offers a path to resolve a number of longstanding issues in general relativity by re-interpreting gravitation as an artifact of torsion rather than curvature. The present work deals with cosmological solutions in an…
Teleparallel gravity models, in which the curvature and the nonmetricity of spacetime are both set zero, are widely studied in the literature. We work a different teleparallel theory, in which the curvature and the torsion of spacetime are…
The Gauss-Bonnet invariant connects foundational aspects of geometry with physical phenomena in a variety of ways. Teleparallel gravity offers a novel direction in which to use the Gauss-Bonnet invariant to go beyond standard cosmology. In…
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 99 (2019) 064006] in which some criticisms on the interpretation of teleparallel…
The superstring and superbrane theories which include gravity as a necessary and fundamental part renew an interest to alternative representations of general relativity as well as the alternative models of gravity. We study the coframe…
Metric-affine geometry provides a non-trivial extension of the general relativity where the metric and connection are treated as the two independent fundamental quantities in constructing the space-time (with non-vanishing torsion and…
Just after Weyl's paper (Weyl in Gravitation und Elektrizit\"at, Sitzungsber. Preuss. Akad., Berlin, 1918) Einstein claimed that a gravity model written in a spacetime geometry with non-metricity suffers from a phenomenon, the so-called…
At the time it celebrates one century of existence, general relativity---Einstein's theory for gravitation---is given a companion theory: the so-called teleparallel gravity, or teleparallelism for short. This new theory is fully equivalent…
A new approach to the description of spin-2 particle in flat and curved spacetime is developed on the basis of the teleparallel gravity theory. We show that such an approach is in fact a true and natural framework for the Fierz…
This thesis investigates modified teleparallel gravity models with a scalar field and teleparallel boundary terms, focusing on their cosmological implications for late-time cosmic acceleration. Teleparallel gravity, is an alternative to…
The discovery of the accelerated expansion of the universe highlighted General Relativity's inability to naturally account for dark energy without invoking a finely tuned cosmological constant. In response, a wide range of alternative…