Non-trivial Minkowski backgrounds in f(T) gravity

TL;DR

This paper investigates non-trivial Minkowski backgrounds in f(T) gravity, revealing that certain Lorentz modes can propagate dynamically, indicating potential additional degrees of freedom and raising questions about the models' viability.

Contribution

It demonstrates the existence of propagating Lorentz modes in non-trivial Minkowski backgrounds within f(T) gravity, a novel finding in Lorentz-violating modified gravity theories.

Findings

Lorentz modes can exhibit non-trivial dynamics

Some modes can propagate in time

Potential additional degrees of freedom in f(T) gravity

Abstract

Boosted and rotated tetrad backgrounds for the Minkowski space are studied in $f(T)$ gravity. We perform Lorentzian perturbations at first order around non-trivial backgrounds and show that some Lorentz modes can exhibit non-trivial dynamics and can propagate in time. This remarkable feature gives evidence of additional mode(s) in the Lorentzian sector which have no precedent in Lorentz-violating modified gravities, however they can cast doubts onto even theoretical viability of these models.