Abstract
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, to a certain limit of a real parameter, in the $f(\bar{R})$ Gravity or, to another limit of the same real parameter, in a modified $f(T)$ Gravity, interpolating between these two theories and still can fall on several other theories. We explicitly show the equivalence with $f(\bar{R})$ Gravity for cases of Friedmann-Lemaitre-Robertson-Walker flat metric for diagonal tetrads, and a metric with spherical symmetry for diagonal and non-diagonal tetrads. We do still four applications, one in the reconstruction of the de Sitter universe cosmological model, for obtaining a static spherically symmetric solution type-de Sitter for a perfect fluid, for evolution of the state parameter $\omega_{DE}$ and for the thermodynamics to the apparent horizon.
Highlights
One of the most important findings in modern physics is that our universe has accelerated expansion [1,2,3]
This approach is known as teleparallel theory (TT) [26,27,28,29], which is demonstrably equivalent to general relativity (GR)
In order to describe the gravitational interaction, and the accelerated expansion of our universe, Ferraro and Fiorini [30] proposed a possible generalization of the TT, which became known as f (T ) gravity [31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62], which up to now has provided good results in both cosmology and local phenomena of gravitation
Summary
One of the most important findings in modern physics is that our universe has accelerated expansion [1,2,3]. It becomes clear that if we do not consider the sign (−) in front of the matter term in the action (9) in the theory, we do not return to GR for a linear f (T ) function, reaching the case opposite to Einstein’s equation This fact will be crucial in showing later that an invariant theory by local Lorentz transformations, as f (R) gravity, cannot fall under f (T ) gravity, since these have opposite coupling signs to the matter term. It is in relation to this problem that we construct a generalization of the teleparallel theory that preserves the invariance of the equations of motion for a local Lorentz transformation
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