Weyl-Cartan-Weitzenböck gravity as a generalization of teleparallel gravity

Abstract

We consider a gravitational model in a Weyl-Cartan space-time, in which the Weitzenböck condition of the vanishing of the sum of the curvature and torsion scalar is also imposed. Moreover, a kinetic term for the torsion is also included in the gravitational action. The field equations of the model are obtained from a Hilbert-Einstein type variational principle, and they lead to a complete description of the gravitational field in terms of two fields, the Weyl vector and the torsion, respectively, defined in a curved background. The cosmological applications of the model are investigated for a particular choice of the free parameters in which the torsion vector is proportional to the Weyl vector. Depending on the numerical values of the parameters of the cosmological model, a large variety of dynamic evolutions can be obtained, ranging from inflationary/accelerated expansions to non-inflationary behaviors. In particular we show that a de Sitter type late time evolution can be naturally obtained from the field equations of the model. Therefore the present model leads to the possibility of a purely geometrical description of the dark energy, in which the late time acceleration of the Universe is determined by the intrinsic geometry of the space-time.

15 pages, 5 figures; title changed, major modifications; accepted for publication in JCAP

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• Conformal symmetry and accelerating cosmology in teleparallel gravity
• Weyl type $f(Q,T)$ gravity, and its cosmological implications
• Structure of neutron, quark and exotic stars in Eddington-inspired Born-Infeld gravity
• Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity
• Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity
• Quantum Cosmology of $f(R,T)$ gravity
• Cosmological implications of modified gravity induced by quantum metric fluctuations
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• Power-law cosmology in Weyl-type $f(Q,T)$ gravity
• Notes on teleparallel cosmology with nonminimally coupled scalar field
• Cosmological tests of the osculating Barthel-Kropina dark energy model
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• Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term
• The Einstein dark energy model
• Bianchi type I cosmological models in Eddington-inspired Born-Infeld gravity
• Cosmological models in $f(T,\mathcal{T})$ gravity and the dynamical system analysis
• Planar Symmetry in f(T) gravity
• Onset of acceleration in a Universe initially filled by dark and baryonic matters in nonminimally coupled teleparallel model
• The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories
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• The Maxwell-Chern-Simons gravity and its cosmological implications
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• Cosmological implications of the Weyl geometric gravity theory
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• Anisotropy in constraint 4D Gauss-Bonnet gravity
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• The general expression for $f(T)$ in a charged cylindrical spacetime with diverse dimensions
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