Metric-affine f(R)-gravity with torsion: an overview

Capozziello, Salvatore; Vignolo, Stefano

doi:10.1002/andp.201010420

Cited by 47 publications

(71 citation statements)

References 23 publications

(39 reference statements)

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“…Equations (3.2a) are by construction symmetric. The symmetrization symbol for the Ricci tensor R ij is omitted because any connection satisfying equations (2.5), (2.6) and (3.2b) gives rise to a Ricci tensor that is automatically symmetric [1,3,4]. We also notice that, if f (R) = kR, we have non-vanishing torsion even if the spin density is zero.…”

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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Section: Geometrical Preliminariesmentioning

confidence: 99%

Dirac fields in f ( R )-gravity with torsion

Fabbri

Vignolo

2011

Class. Quantum Grav.

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“…This is a direct consequence of the new field equations which can lead to the existence of additional radiative modes. Using a linearized approach, several studies investigated the additional polarization modes in all versions of f (R) theories ( [10][11][12][13][14][15], or more recently [16]) and scalar-tensor theories [17], and it has been shown that only one massive longitudinal mode exists along with the two usual tensorial modes of GR. In addition to the linearized approach, another powerful tool to study the properties of GWs in any metric theory is the Newman-Penrose (NP) approach developed by Eardley et al [18,19].…”

Section: Introductionmentioning

confidence: 99%

Gravitational wave polarization modes inf(R)theories

2016

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Many studies have been carried out in the literature to evaluate the number of polarization modes of gravitational waves in modified theories, in particular in f(R) theories. In the latter ones, besides the usual two transverse-traceless tensor modes present in general relativity, there are two additional scalar ones: a massive longitudinal mode and a massless transverse mode (the so-called breathing mode). This last mode has often been overlooked in the literature, due to the assumption that the application of the Lorenz gauge implies transverse-traceless wave solutions. We however show that this is in general not possible and, in particular, that the traceless condition cannot be imposed due to the fact that we no longer have a Minkowski background metric. Our findings are in agreement with the results found using the Newman-Penrose formalism and thus clarify the inconsistencies found so far in the literature. Many studies have been carried out in the literature to evaluate the number of polarization modes of gravitational waves in modified theories, in particular in f (R) theories. In the latter ones, besides the usual two transverse-traceless tensor modes present in general relativity, there are two additional scalar ones: a massive longitudinal mode and a massless transverse mode (the so-called breathing mode). This last mode has often been overlooked in the literature, due to the assumption that the application of the Lorenz gauge implies transverse-traceless wave solutions. We however show that this is in general not possible and, in particular, that the traceless condition cannot be imposed due to the fact that we no longer have a Minkowski background metric. Our findings are in agreement with the results found using the Newman-Penrose formalism, and thus clarify the inconsistencies found so far in the literature.

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“…As discussed in [12,13], the Cartan torsion tensor plays the role of spin source in the gravitational field equations where the affine connection is not simply Levi-Civita. Furthermore, as demonstrated in [106,[117][118][119], torsion plays an important role in Extended Theories of Gravity since brings further gravitational degrees of freedom responsible of chiral interactions. In other words, torsion is not only the source of spin but, thanks to the non-trivial structure of connections Γ α βγ , can give rise to chiral interactions of geometric origin [120].…”

Section: Gl(4)mentioning

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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Metric-affine f(R)-gravity with torsion: an overview

Cited by 47 publications

References 23 publications

Dirac fields in f ( R )-gravity with torsion

Dirac fields in f ( R )-gravity with torsion

Gravitational wave polarization modes inf(R)theories

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

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