https://doi.org/10.1140/epjc/s10052-016-4220-8
Regular Article - Theoretical Physics
Generalized teleparallel theory
1
Faculdade de Física, PPGF, Universidade Federal do Pará, Belém, Pará, 66075-110, Brazil
2
Faculdade de Engenharia da Computação, Universidade Federal do Pará, Campus Universitrio de Tucuruí, Tucuruí, Pará, CEP: 68464-000, Brazil
3
Faculdade de Ciências Exatas e Tecnologia, Universidade Federal do Pará, Campus Universitário de Abaetetuba, Abaetetuba, Pará, CEP: 68440-000, Brazil
* e-mail: esialg@gmail.com
Received:
6
November
2015
Accepted:
22
June
2016
Published online:
6
July
2016
We construct a theory in which the gravitational interaction is described only by torsion, but that generalizes the teleparallel theory still keeping the invariance of local Lorentz transformations in one particular case. We show that our theory falls, in a certain limit of a real parameter, under 
gravity or, in another limit of the same real parameter, under modified f(T) gravity; on interpolating between these two theories it still can fall under several other theories. We explicitly show the equivalence with gravity for the cases of a Friedmann–Lemaître–Robertson–Walker flat metric for diagonal tetrads, and a metric with spherical symmetry for diagonal and non-diagonal tetrads. We study four applications, one in the reconstruction of the de Sitter universe cosmological model, for obtaining a static spherically symmetric solution of de Sitter type for a perfect fluid, for evolution of the state parameter 
, and for the thermodynamics of the apparent horizon.
© The Author(s), 2016
