Problems with Propagation and Time Evolution in f(T) Gravity

TL;DR

This paper investigates theoretical issues in f(T) gravity, revealing potential superluminal modes and problems with the evolution of initial conditions, which challenge its viability as an alternative to general relativity.

Contribution

It identifies fundamental problems in generic f(T) gravity, including superluminal propagation and non-uniqueness of evolution, using characteristic equations and Hamiltonian analysis.

Findings

Superluminal propagating modes can occur in f(T) gravity.

The Cauchy problem in FLRW spacetime is ill-posed in f(T) gravity.

These issues suggest theoretical inconsistencies in f(T) gravity.

Abstract

Teleparallel theories of gravity have a long history. They include a special case referred to as the Teleparallel Equivalent of General Relativity (TEGR, aka GR$_{\|}$). Recently this theory has been generalized to f(T) gravity. Tight constraints from observations suggest that f(T) gravity is not as robust as initially hoped. This might hint at hitherto undiscovered problems at the theoretical level. In this work, we point out that a generic f(T) theory can be expected to have certain problems including superluminal propagating modes, the presence of which can be revealed by using the characteristic equations that govern the dynamics in f(T) gravity and/or the Hamiltonian structure of the theory via Dirac constraint analysis. We use several examples from simpler gauge field theories to explain how such superluminal modes could arise. We also point out problems with the Cauchy development of a constant time hypersurface in FLRW spacetime in f(T) gravity. The time evolution from a FLRW (and as a special case, Minkowski spacetime) initial condition is not unique.