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

We consider a gravitational model in a Weyl-Cartan space-time in which the Weitzenbock condition of the vanishing of the sum of the curvature and torsion scalar is imposed. In contrast to the standard teleparallel theories, our model is formulated in a four-dimensional curved spacetime. The properti...

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Bibliographic Details
Published in:Journal of cosmology and astroparticle physics 2012-10, Vol.2012 (10), p.i-22
Main Authors: Haghani, Zahra, Harko, Tiberiu, Sepangi, Hamid Reza, Shahidi, Shahab
Format: Article
Language:English
Subjects:
ACCELERATION
APPROXIMATIONS
ASTROPHYSICS, COSMOLOGY AND ASTRONOMY
COSMOLOGICAL MODELS
COSMOLOGY
Curved
DE SITTER GROUP
DE SITTER SPACE
Evolution
FIELD EQUATIONS
FOUR-DIMENSIONAL CALCULATIONS
Gravitation
GRAVITATIONAL FIELDS
Mathematical analysis
Mathematical models
NONLUMINOUS MATTER
POISSON EQUATION
SCALARS
SPACE-TIME
TORSION
UNIVERSE
VARIATIONAL METHODS
VECTOR FIELDS
Vectors (mathematics)
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Summary:We consider a gravitational model in a Weyl-Cartan space-time in which the Weitzenbock condition of the vanishing of the sum of the curvature and torsion scalar is imposed. In contrast to the standard teleparallel theories, our model is formulated in a four-dimensional curved spacetime. The properties of the gravitational field are then described by the torsion tensor and Weyl vector fields. 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, dehned 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. The Newtonian limit of the model is also considered, and it is shown that the Poisson equation can be recovered in the weak field approximation. Depending on the numerical values of the parameters of the cosmological model, a large variety of dynamic evolutions can be obtained, ranging from inhationary/accelerated expansions to non-inhationary 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.
ISSN:1475-7516
1475-7516
DOI:10.1088/1475-7516/2012/10/061