Generalized teleparallel theory

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, in a certain limit of a real parameter, under f (R) 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 f (R) 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 ω DE , and for the thermodynamics of the apparent horizon.

New observational constraints onf(T) gravity from cosmic chronometers

“…That is why f (T ) gravity and its cosmological applications have gained a lot of interest in the literature, both for early-time [24][25][26][27][28] and late-time descriptions. Finally, one can construct various extensions of f (T ) gravity and investigate their interesting cosmological implications [67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83].…”

Solar system tests for realistic f(T) models with non-minimal torsion–matter coupling

“…TEGR [3][4][5] (13) will give the same spacetime metric. Though this does not make much difference in TEGR, it does have some significant effects on f (T ) theories, one of which is that the f (T ) theories are no longer Lorentz invariant theories [48].…”

“…One possible scheme is f (T ) theory, in which the torsion scalar T in the a e-mail: zhaixh@shnu.edu.cn b e-mail: kychz@shnu.edu.cn gravitation Lagrangian is replaced by an arbitrary function f (T ) [8][9][10][11][12][13][14]. Compared to f (R) theory, the field equations are second order instead of fourth one, which is an important advantage of f (T ) theory.…”

“…Under the framework of TEGR, different modification of gravity theory has been proposed for better understanding of the currently accelerating universe [4,5]. One possible scheme is f (T ) theory, in which the torsion scalar T in the gravitation Lagrangian is replaced by an arbitrary function f (T ) [6][7][8][9][10]. Compared to f (R) theory, the field equations are second order instead of fourth one, which is an important advantage of f (T ) theory.…”

Regular black holes inf(R)gravity coupled to nonlinear electrodynamics

“…The f (T ) theory is the analogous of the f (R) gravity whose modification was introduced to try to account for the same problems of GR (see [19] for a list of references). Further generalizations are the f (T, Θ) [20], the f (T, T G ) [21], and the f (T ) gravity theories [22]. For a review on the applications of modified theories of gravity see, e.g., Ref.…”