f(R) GRAVITY WITH TORSION: A GEOMETRIC APPROACH WITHIN THE $\mathcal{J}$-BUNDLES FRAMEWORK

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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“…These considerations can be easily extended to any function of L R as in [105]. Observe that the second term is a divergence and may be ignored.…”

Section: Field Equations For Poincaré Gravitymentioning

confidence: 99%

“…The lowest order gravitational action is one that is linear in the curvature scalar while being quadratic in torsion. However, the scheme can be immediately extended to more general gravitational theories as in [105].…”

Section: Field Equations For Poincaré Gravitymentioning

confidence: 99%

f(T) teleparallel gravity and cosmology

et al. 2016

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“…3 f (R)-gravity with torsion and conservation laws f (R)-gravity with torsion can be formulated in the metric-affine approach [1] or in the tetrad-affine one [2]. In the first case, the gravitational dynamical fields are represented by the metric g and a metric compatible connection Γ on the spacetime manifold M .…”

Section: Geometrical Preliminariesmentioning

confidence: 99%

“…On the other hand, in case of coupling with spin matter, for instance spinor fields, the tetrad-affine formulation is more suitable. The corresponding field equations have been derived in [2] (see also [5]) and turn out to be ∂Lm ∂ω µν i e µ t e ν s e α i are the stress-energy and spin density tensors of the matter field. From equation (3.3b) it is seen that, in presence of ω-dependent matter, there are two sources of torsion: the spin density S α ts and the non-linearity of the gravitational Lagrangian.…”

Section: Geometrical Preliminariesmentioning

confidence: 99%

Dirac fields in f ( R )-gravity with torsion

Fabbri

Vignolo

2011

Class. Quantum Grav.

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We study f (R)-gravity with torsion in presence of Dirac massive fields. Using the Bianchi identities, we formulate the conservation laws of the theory and we check the consistency with the matter field equations. Further, we decompose the field equations in torsionless and torsional terms: we show that the nonlinearity of the gravitational Lagrangian reduces to the presence of a scalar field that depends on the spinor field; this additional scalar field gives rise to an effective stress-energy tensor and plays the role of a scale factor modifying the normalization of Dirac fields. Problems for fermions regarding the positivity of energy and the particle-antiparticle duality are discussed.

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“…Such geometrical identities work in every covariant field theory (e.g. Electromagnetism or GR) and can be read as equations of motion also in a fiber bundle approach [106]. We want to show that, the absolute validity of conservation laws, intrinsically contains symmetric dynamics; moreover, reducing dynamics from 5D to 4D, it gives rise to the physical quantities characterizing particles as the mass.…”

Section: While the Gauge Groups Involved In The Standardmentioning

confidence: 99%

Deriving the mass of particles from Extended Theories of Gravity in LHC era

Capozziello

Basini

2011

Eur. Phys. J. C

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We derive a geometrical approach to produce the mass of particles that could be suitably tested at LHC. Starting from a 5D unification scheme, we show that all the known interactions could be suitably deduced as an induced symmetry breaking of the non-unitary GL(4)-group of diffeomorphisms. The deformations inducing such a breaking act as vector bosons that, depending on the gravitational mass states, can assume the role of interaction bosons like gluons, electroweak bosons or photon. The further gravitational degrees of freedom, emerging from the reduction mechanism in 4D, eliminate the hierarchy problem since generate a cut-off comparable with electroweak one at TeV scales. In this "economic" scheme, gravity should induce the other interactions in a non-perturbative way.

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f(R) GRAVITY WITH TORSION: A GEOMETRIC APPROACH WITHIN THE $\mathcal{J}$-BUNDLES FRAMEWORK

Cited by 39 publications

References 38 publications

f(T) teleparallel gravity and cosmology

f(T) teleparallel gravity and cosmology

Dirac fields in f ( R )-gravity with torsion

Deriving the mass of particles from Extended Theories of Gravity in LHC era

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