Spin connection and renormalization of teleparallel action

Krššák, Martin; Pereira, J. G.

doi:10.1140/epjc/s10052-015-3749-2

Cited by 77 publications

(133 citation statements)

References 22 publications

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“…It should be remarked, however, that both of them transform covariantly under global tangent-space Lorentz transformations. The lack of a local Lorentz covariance in the tetrad teleparallel gravity can be considered as the teleparallel manifestation of the pseudotensor character of the gravitational energy-momentum density of GR [121,[126][127][128].…”

Section: Gravitational Energy-momentum Currentmentioning

confidence: 99%

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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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Section: Gravitational Energy-momentum Currentmentioning

confidence: 99%

“…Note the interesting feature that in simple TEGR this is not the case, even if one keeps a non-zero spin connection. In order to see this, one starts by explicitly writing the torsion scalar as [126][127][128] T (e…”

Section: Restoring Local Lorentz Invariance In F (T ) Gravitymentioning

confidence: 99%

f(T) teleparallel gravity and cosmology

et al. 2016

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“…As we notice, in the GR limit the terms violating local Lorentz invariance also vanish in the general field equations, so in the models where GR is an attractor, the problematic degrees of freedom get dynamically suppressed by the cosmological evolution. A very recent proposal to recover local Lorentz invariance is to formulate the theory in a covariant way [15] by including purely inertial spin connection (still leading to zero curvature), carefully delineating the effects of gravitation and inertia [16]. Since the flat FLRW tetrad in Cartesian coordinates is already "proper" [15], we can expect the ensuing cosmological equations not to get additional spin connection contributions and our results will still be valid in the putative covariant formulation of scalartorsion gravity.…”

Section: Introductionmentioning

confidence: 74%

General relativity as an attractor for scalar-torsion cosmology

Järv

Toporensky

2016

Phys. Rev. D

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We study flat Friedmann-Lemaître-Robertson-Walker cosmological models for a scalar field coupled nonminimally to teleparallel gravity with generic coupling and potential functions. The goal of this paper is to determine the conditions under which cosmological evolution tends to the limit where the variation of the gravitational "constant" ceases and the system evolves close to general relativity. These conditions can be read off from the approximate analytical solutions describing the process in matter and potential domination eras. Only those models where the GR limit exists and is an attractor can be considered viable. We expect the results to hold in the original "pure tetrad" formulation as well as in the recently suggested covariant formulation of the teleparallel theory. In the former case the GR attractor simultaneously provides a mechanism how cosmological evolution suppresses the problematic degrees of freedom stemming from the lack of local Lorentz invariance.PACS numbers: 04.50. Kd, 95.36.+x

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“…This is relevant, for example, in theoretical models of calm stars, idealized galaxies, or any distribution of matter which may be approximated as spherical and time independent. We take the following tetrad 8) which is compatible with the well-known following metric:…”

Section: Case I: Static Spherical Symmetrymentioning

confidence: 99%

“…Therefore, in that version of the theory one must choose a metric compatible tetrad which also yields zero for the components ω a bν . If this is not done correctly, then one is inadvertently including inertial (non-gravitational) effects into the resulting equations of motion [8], [9]. This is essentially the origin of the "non-Lorentz covariance" of traditional F (T ) gravity [9], [10], [11], [12], [13] [14], and leads one to having to choose a "good" tetrad [15], [16].…”

Section: Introductionmentioning

confidence: 99%

Junction conditions forF(T)gravity from a variational principle

Velay‐Vitow

DeBenedictis

2017

Phys. Rev. D

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We derive a general set of acceptable junction conditions for F (T ) gravity via the variational principle. The analysis is valid for both the traditional form of F (T ) gravity theory as well as the more recently introduced Lorentz covariant theory of Krššák and Saridakis. We find that the general junction conditions derived, when applied to simple cases such as highly symmetric static or time dependent geometries (such as spherical symmetry) imply both the Synge junction conditions as well as the Israel-Sen-LanczosDarmois junction conditions of General Relativity. In more complicated scenarios the junction conditions derived do not generally imply the well-known junction conditions of General Relativity. However, the junctions conditions of de la Cruz-Dombriz, Dunsby, and Sáez-Gómez make up an interesting subset of this more general case.PACS (2010)

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Spin connection and renormalization of teleparallel action

Cited by 77 publications

References 22 publications

f(T) teleparallel gravity and cosmology

f(T) teleparallel gravity and cosmology

General relativity as an attractor for scalar-torsion cosmology

Junction conditions forF(T)gravity from a variational principle

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