Non trivial frames for f(T) theories of gravity and beyond

TL;DR

This paper investigates conceptual challenges in f(T) gravity theories, focusing on the difficulties in defining physically meaningful frames due to broken local Lorentz invariance, exemplified through cosmological models.

Contribution

It highlights the issues with autoparallel frames in f(T) theories and provides explicit vierbein solutions for cosmological spacetimes.

Findings

Autoparallel frames in f(T) theories are difficult to interpret physically.

Explicit vierbein fields are constructed for Friedmann-Robertson-Walker cosmologies.

Broken local Lorentz invariance complicates the understanding of these theories.

Abstract

Some conceptual issues concerning $f(T)$ theories --a family of modified gravity theories based on absolute parallelism-- are analyzed. Due to the lack of local Lorentz invariance, the autoparallel frames satisfying the field equations are evasive to an \emph{a priori} physical understanding. We exemplify this point by working out the vierbein (tetrad) fields for closed and open Friedmann-Robertson-Walker cosmologies.