Degrees of freedom of $f(T)$ gravity

Abstract

We investigate the Hamiltonian formulation of $f(T)$ gravity and find that there are five degrees of freedom. The six first class constraints corresponding to the local Lorentz transformation in Teleparallel gravity become second class constraints in $f(T)$ gravity, which leads to the appearance of three extra degrees of freedom and the violation of the local Lorentz invariance in $f(T)$ gravity. In general, there are $D-1$ extra degrees of freedom for $f(T)$ gravity in $D$ dimensions, and this implies that the extra degrees of freedom correspond to one massive vector field or one massless vector field with one scalar field.

18 pages, some references added, minor revision to appear in JHEP

References in corpus (15)

• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• On Born-Infeld Gravity in Weitzenbock spacetime
• Cosmological perturbations in f(T) gravity
• Observational constraints on $f(T)$ theory
• f(T) gravity mimicking dynamical dark energy. Background and perturbation analysis
• Generalizations of teleparallel gravity and local Lorentz symmetry
• $f(T)$ models with phantom divide line crossing
• Growth factor in f(T) gravity
• Cosmological evolution in exponential gravity
• Translation of Einstein's Attempt of a Unified Field Theory with Teleparallelism
• Pure kinetic k-essence as the cosmic speed-up
• Comment on "Einstein's Other Gravity and the Acceleration of the Universe''
• Hamiltonian formulation of unimodular gravity in the teleparallel geometry