Generalized Teleparallel Theory

TL;DR

This paper introduces a generalized teleparallel gravity theory that interpolates between $f(ar{R})$ and $f(T)$ gravities, maintaining local Lorentz invariance in specific cases and demonstrating its equivalence with $f(ar{R})$ gravity in cosmological and spherically symmetric scenarios.

Contribution

The paper develops a new generalized teleparallel gravity framework that unifies and extends existing $f(ar{R})$ and $f(T)$ theories, preserving local Lorentz invariance in particular limits.

Findings

Equivalent to $f(ar{R})$ gravity in FLRW flat metric with diagonal tetrads

Represents a modified $f(T)$ gravity in certain parameter limits

Successfully models de Sitter universe and static spherically symmetric solutions

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.