Local symmetries and physical degrees of freedom in $f(T)$ gravity: a Dirac Hamiltonian constraint analysis

TL;DR

This paper performs a detailed Hamiltonian analysis of $f(T)$ gravity, clarifying the status of local Lorentz invariance and the number of physical degrees of freedom, revealing potential issues with propagating modes.

Contribution

It provides a comprehensive Hamiltonian constraint analysis of $f(T)$ gravity, establishing the number of degrees of freedom and the conditions under which Lorentz invariance is broken.

Findings

Number of physical degrees of freedom is 5 in 4D.

Lorentz invariance can be broken in various scenarios.

Diffeomorphism invariance is explicitly confirmed.

Abstract

In the literature on $f(T)$ gravity, the status of local Lorentz invariance and the number of physical degrees of freedom have been controversial issues. Relying on a detailed Hamiltonian analysis, we show that there are several scenarios describing how local Lorentz invariance can be broken, but in the generic case, the number of physical degrees of freedom is found to be $N^*=5$; in $D$ dimensions, this number is $N^*=D(D-3)/2+(D-1)$. As expected, the theory is vulnerable to having problematical propagating modes. We compare our results with those existing in the literature. As a byproduct of our analysis, the diffeomorphysm invariance is explicitly confirmed.