f(T) Gravity and local Lorentz invariance

TL;DR

This paper investigates f(T) gravity theories, revealing they lack local Lorentz invariance and possess extra degrees of freedom, challenging their viability as alternatives to general relativity for explaining cosmic acceleration.

Contribution

It demonstrates that generalised teleparallel gravity theories are not invariant under local Lorentz transformations and identifies additional degrees of freedom, clarifying misconceptions in recent literature.

Findings

f(T) theories lack local Lorentz invariance

Extra degrees of freedom are present in these theories

The teleparallel Lagrangian equivalent to GR is an exception

Abstract

We show that in theories of generalised teleparallel gravity, whose Lagrangians are algebraic functions of the usual teleparallel Lagrangian, the action and the field equations are not invariant under local Lorentz transformations. We also argue that these theories appear to have extra degrees of freedom with respect to general relativity. The usual teleparallel Lagrangian, which has been extensively studied and leads to a theory dynamically equivalent to general relativity, is an exception. Both of these facts appear to have been overlooked in the recent literature on f(T) gravity, but are crucial for assessing the viability of these theories as alternative explanations for the acceleration of the universe.