Teleparallel theories of gravity have a long history. They include a special case referred to as the teleparallel equivalent of general relativity (TEGR, also known as ${\mathrm{GR}}_{\parallel }$). 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 Friedmann-Lemaître-Roberson-Walker (FLRW) spacetime in $f(T)$ gravity. The time evolution from a FLRW (and as a special case, Minkowski spacetime) initial condition is not unique.

• Received 19 April 2013

DOI:https://doi.org/10.1103/PhysRevD.88.024019