Degrees of Freedom in modified Teleparallel Gravity

TL;DR

This paper investigates the degrees of freedom in modified teleparallel gravity, highlighting issues with local symmetry breaking, strong coupling, and discrepancies in Hamiltonian analyses, and advocates for studying general models despite ghost concerns.

Contribution

It provides a detailed analysis of the degrees of freedom and symmetry breaking in modified teleparallel gravity, clarifying discrepancies in existing perturbation analyses and proposing broader model studies.

Findings

Linear perturbation treatments underestimate dynamical degrees of freedom.

Hamiltonian analyses show complex and sometimes contradictory results.

General models may contain more physical degrees of freedom than previously recognized.

Abstract

I discuss the issue of degrees of freedom in modified teleparallel gravity. These theories do have an extra structure on top of the usual (pseudo)Riemannian manifold, that of a flat parallel transport. This structure is absolutely abstract and unpredictable (pure gauge) in GR-equivalent models, however it becomes physical upon modifications. The problem is that, in the most popular models, this local symmetry is broken but not stably so, hence the infamous strong coupling issues. The Hamiltonian analyses become complicated and with contradictory results. A funny point is that what we see in available linear perturbation treatments of $f(T)$ gravity is much closer to the analysis with less dynamical degrees of freedom which has got a well-known mistake in it, while the more accurate work predicts much more of dynamics than what has ever been seen up to now. I discuss possible reasons behind this puzzle, and also argue in favour of studying the most general New GR models which are commonly ignored due to suspicion of ghosts.