Degrees of freedom and Hamiltonian formalism for $f(T)$ gravity

TL;DR

This paper investigates the extra degree of freedom in $f(T)$ gravity using a toy model to understand its origin related to pseudoinvariance under local symmetry, building on recent Hamiltonian analyses.

Contribution

It introduces a toy model illustrating the key feature of $f(T)$ gravity's extra degree of freedom and clarifies its connection to pseudoinvariance and local symmetry.

Findings

The toy model captures the essential feature of $f(T)$ gravity.

The extra degree of freedom is linked to pseudoinvariance under local symmetry.

Provides insight into the Hamiltonian structure of $f(T)$ gravity.

Abstract

The existence of an extra degree of freedom (d.o.f.) in $f(T)$ gravity has been recently proved by means of the Dirac formalism for constrained Hamiltonian systems. We will show a toy model displaying the essential feature of $f(T)$ gravity, which is the pseudoinvariance of T under a local symmetry, to understand the nature of the extra d.o.f.