Teleparallel equivalent of Gauss-Bonnet gravity and its modifications

Kofinas, Georgios; Saridakis, Emmanuel N.

doi:10.1103/physrevd.90.084044

Cited by 247 publications

(188 citation statements)

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“…Nevertheless, the asymptotic frame (594) is also not adequate to globally describe the Schwarzschild geometry, as can be checked by replacing it in the equations of motion (587). Hence, one needs to seek for a Lorentz transformation in such a way that acting on (594) to obtain a non-diagonal vierbein able to achieve a null torsion scalar T .…”

Section: Black Holes and Other Solutionsmentioning

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: Black Holes and Other Solutionsmentioning

confidence: 99%

“…Hence, inspired by this strategy, in [587] the authors followed the same steps for the Gauss-Bonnet combination, which as it is well known reads as:…”

Section: B F (T Tg) Gravitymentioning

confidence: 99%

f(T) teleparallel gravity and cosmology

et al. 2016

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“…Hence, f (T ) gravity has novel and interesting cosmological implications . Additionally, note that if one starts from TEGR, but instead of the f (R) is inspired by higher-curvature modifications of General Relativity, one can construct higher-order torsion gravity, such as the f (T, T G ) paradigm [56,57], which also presents interesting cosmological behavior. Finally, another modification of TEGR is to extend it inserting the Weitzenböck condition in a Weyl-Cartan geometry via a Lagrange multiplier, with interesting cosmological implications [58,59].…”

Section: Contents 1 Introductionmentioning

confidence: 99%

f(T,𝒯) gravity and cosmology

Harkó

Lobo

Otalora

et al. 2014

J. Cosmol. Astropart. Phys.

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259

213

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Abstract. We present an extension of f (T ) gravity, allowing for a general coupling of the torsion scalar T with the trace of the matter energy-momentum tensor T . The resulting f (T, T ) theory is a new modified gravity, since it is different from all the existing torsion or curvature based constructions. Applied to a cosmological framework, it leads to interesting phenomenology. In particular, one can obtain a unified description of the initial inflationary phase, the subsequent non-accelerating, matter-dominated expansion, and then the transition to a late-time accelerating phase. Additionally, the effective dark energy sector can be quintessence or phantom-like, or exhibit the phantom-divide crossing during the evolution. Moreover, in the far future the universe results either to a de Sitter exponential expansion, or to eternal power-law accelerated expansions. Finally, a detailed study of the scalar perturbations at the linear level reveals that f (T, T ) cosmology can be free of ghosts and instabilities for a wide class of ansatzes and model parameters.

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“…Various cosmological features of this theory have been investigated like solar system constraints, static wormhole solutions, discussion of Birkhoff 's theorem, instability ranges of collapsing stars, and many more [6][7][8]. Recently, a well-known modified version of ( ) theory is proposed by involving higher order torsion correction terms named as ( , ) theory depending upon and [9]. This is a completely different theory which does not correspond to ( ) as well as any other modified theory.…”

Section: Introductionmentioning

confidence: 99%

Lorentz Distributed Noncommutative F(T,TG) Wormhole Solutions

Sharif

Nazir

2018

Advances in High Energy Physics

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The aim of this paper is to study static spherically symmetric noncommutative ( , ) wormhole solutions along with Lorentzian distribution. Here, and are torsion scalar and teleparallel equivalent Gauss-Bonnet term, respectively. We take a particular redshift function and two ( , ) models. We analyze the behavior of shape function and also examine null as well as weak energy conditions graphically. It is concluded that there exist realistic wormhole solutions for both models. We also studied the stability of these wormhole solutions through equilibrium condition and found them stable.

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Teleparallel equivalent of Gauss-Bonnet gravity and its modifications

Cited by 247 publications

References 86 publications

f(T) teleparallel gravity and cosmology

f(T) teleparallel gravity and cosmology

f(T,𝒯) gravity and cosmology

Lorentz Distributed Noncommutative F(T,TG) Wormhole Solutions

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