Teleparallel Gravity: An Overview

Andrade, V. C. de; Guillen, L. C. T.; Pereira, J. G.

doi:10.1142/9789812777386_0144

Cited by 62 publications

(100 citation statements)

References 7 publications

(12 reference statements)

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“…It corresponds to a gauge theory for the translation group [55,111,112,114,115]. It was first introduced by Einstein himself as an equivalent alternative to GR [116].…”

Section: Teleparallel Gravitymentioning

confidence: 99%

f(T) teleparallel gravity and cosmology

et al. 2016

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Over the past decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f (T ) gravity, where f (T ) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f (T ) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f (T ) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, alternative to a cosmological constant, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, for a certain class of f (T ) models, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations, or alternatively, the Big Bang singularity can be avoided at even earlier moments due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f (T ) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f (T ) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f (R) gravity, trying to enlighten the subject of which formulation, or combination of formulations, might be more suitable for quantization ventures and cosmological applications. Contents

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“…It corresponds to a gauge theory for the translation group [55,111,112,114,115]. It was first introduced by Einstein himself as an equivalent alternative to GR [116].…”

Section: Teleparallel Gravitymentioning

confidence: 99%

f(T) teleparallel gravity and cosmology

et al. 2016

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“…µν is the contortion tensor and cν is the basic vector of the AP-space, is known as the Teleparallel Equivalent of GR (TEGR)(cf. [1,9]). This is because, one can easily show that, apart from a divergence term, one can write:…”

Section: Conservation Of Matter-energy Is Guaranteed Via Using Bianchmentioning

confidence: 99%

Unification Principle and a Geometric Field Theory

2015

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Abstract:In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.

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“…In order to revisit the WIMT we shall use some elements of Weitzenböck geometry [15,16]. The Weitzenböck connection is …”

Section: Weitzenböck Geometry and Vielbeinsmentioning

confidence: 99%

WIMT in Gullstränd–Painlevé and Reissner–Nordström metrics: induced stable gravito-magnetic monopoles

Romero

Bellini

2015

Eur. Phys. J. C

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The aim of this work is to apply Weitzeböck Induced Matter Theory (WIMT) to Gullstränd-Painlevé and Reissner-Nordström metrics in the framework of WIMT. This is a newly developed method that extends Induced Matter Theory from a curved 5D manifold using the Weitzeböck's geometry, using the fact that the Riemann-Weitzenböck curvature tensor is always null. We obtain the presence of currents whose interpretation can lead to the presence of stable gravito-magnetic monopoles.

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Teleparallel Gravity: An Overview

Cited by 62 publications

References 7 publications

f(T) teleparallel gravity and cosmology

f(T) teleparallel gravity and cosmology

Unification Principle and a Geometric Field Theory

WIMT in Gullstränd–Painlevé and Reissner–Nordström metrics: induced stable gravito-magnetic monopoles

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