Irreducible decompositions of nonmetricity, torsion, curvature and Bianchi identities in metric-affine spacetimes

McCrea, J. D.

doi:10.1088/0264-9381/9/2/018

Cited by 74 publications

(73 citation statements)

References 24 publications

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“…For the sake of brevity, in the following, we will refer respectively to the tensor (20) as a V-torsion, to the tensor (21) as an A-torsion and to the tensor (22) as a T-torsion. Finally, the dual operation (see [51,55]) defined as…”

Section: Decomposition Of Torsion In U4mentioning

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: Decomposition Of Torsion In U4mentioning

confidence: 99%

“…A decomposition of torsion into irreducible tensors is given also in [51,52]. For a systematic account, see [55].…”

Section: The Raychaudhuri Equationmentioning

confidence: 99%

f(T) teleparallel gravity and cosmology

et al. 2016

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“…Numbers in parentheses in front of quantities correspond to the irreducible decompositions performed in [8].…”

Section: Lagrangian Gauge and Matter Currentsmentioning

confidence: 99%

A cosmological model in Weyl$ndash$Cartan spacetime: I. Field equations and solutions

Puetzfeld¹

2002

Class. Quantum Grav.

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Abstract. In this first article of a series on alternative cosmological models we present an extended version of a cosmological model in Weyl-Cartan spacetime. The new model can be viewed as a generalization of a model developed earlier jointly with Tresguerres. Within this model the non-Riemannian quantities, i.e. torsion T α and nonmetricity Q αβ , are proportional to the Weyl 1-form. The hypermomentum ∆ αβ depends on our ansatz for the nonmetricity and vice versa. We derive the explicit form of the field equations for different cases and provide solutions for a broad class of parameters. We demonstrate that it is possible to construct models in which the non-Riemannian quantities die out with time. We show how our model fits into the more general framework of metric-affine gravity (MAG).

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“…This comes about as follows: In n-dimensions, the torsion can be decomposed into 3 irreducible pieces, a tensor, a vector, and an axial vector piece, see [19]. In 2 dimensions torsion is irreducible and only the (co-)vector piece survives:…”

Section: Complete Integrability Of Quadratic Pg Lagrangians In Two DImentioning

confidence: 99%

Towards complete integrability of two-dimensional Poincaré gauge gravity

et al. 1993

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It is shown that gravity on the line can be described by the two dimensional (2D) Hilbert-Einstein Lagrangian supplemented by a kinetic term for the coframe and a translational boundary term. The resulting model is equivalent to a Yang-Mills theory of local translations and frozen Lorentz gauge degrees. We will show that this restricted Poincaré gauge model in 2 dimensions is completely integrable. Exact wave, charged black hole, and 'dilaton' solutions are then readily found. In vacuum, the integrability of the general 2D Poincaré gauge theory is formally proved along the same line of reasoning.

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Irreducible decompositions of nonmetricity, torsion, curvature and Bianchi identities in metric-affine spacetimes

Cited by 74 publications

References 24 publications

f(T) teleparallel gravity and cosmology

f(T) teleparallel gravity and cosmology

A cosmological model in Weyl$ndash$Cartan spacetime: I. Field equations and solutions

Towards complete integrability of two-dimensional Poincaré gauge gravity

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