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

Cited by in corpus (94)

• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Teleparallel Gravity: From Theory to Cosmology
• New Horizons for Fundamental Physics with LISA
• $f(T,\mathcal{T})$ gravity and cosmology
• Good and bad tetrads in f(T) gravity
• Nonminimal torsion-matter coupling extension of f(T) gravity
• Exact charged black-hole solutions in D-dimensional f(T) gravity: torsion vs curvature analysis
• Anisotropic Universe Models in f(T) Gravity
• Energy conditions bounds on f(T) gravity
• Attractor Solutions in f(T) Cosmology
• Weak-Field Spherically Symmetric Solutions in $f(T)$ gravity
• Bayesian analysis of $f(T)$ gravity using $f{\sigma }_8$ data
• Stability of a non-minimally conformally coupled scalar field in F(T) cosmology
• Dynamical features of scalar-torsion theories
• Noether symmetry of F(T) cosmology with quintessence and phantom scalar fields
• Remnant group of local Lorentz transformations in f(T) theories
• Dynamical systems approach and generic properties of $f(T)$ cosmology
• $f(T)$ gravitational baryogenesis
• Local symmetries and physical degrees of freedom in $f(T)$ gravity: a Dirac Hamiltonian constraint analysis
• Conformal Gravity and Transformations in the Symmetric Teleparallel Framework
• Modified gravity: a unified approach
• Energy conditions in generalized teleparallel gravity models
• Traversable wormholes in the extended teleparallel theory of gravity with matter coupling
• Foundational issues in f(T) gravity theory
• Review of the Hamiltonian analysis in teleparallel gravity
• Minkowski space in $f(T)$ gravity
• Statefinder Analysis of f(T) Cosmology
• Kerr geometry in f(T) gravity
• ADM formulation and Hamiltonian analysis of $f(Q)$ gravity
• Non-trivial Minkowski backgrounds in f(T) gravity
• Remnant Symmetry, Propagation and Evolution in f(T) Gravity
• On the gauge fixing in the Hamiltonian analysis of general teleparallel theories
• Bianchi identities in f(T) gravity: paving the way to confrontation with astrophysics
• Higgs inflation and teleparallel gravity
• First Order Formalism for Thick Branes in Modified Teleparallel Gravity
• The effective field theory approach to the strong coupling issue in $f(T)$ gravity
• Cosmological perturbations in modified teleparallel gravity models: Boundary term extension
• Parameterized post-Newtonian limit of general teleparallel gravity theories
• Analyzing the geometrical and dynamical parameters of modified Teleparallel-Gauss-Bonnet model
• Toward a concordance teleparallel Cosmology I: Background Dynamics
• Logamediate Inflation in f(T) Teleparallel Gravity
• Spontaneous Lorentz symmetry-breaking constraints in Kalb-Ramond gravity
• McVittie solution in f(T) gravity
• Dirac-Bergmann analysis and Degrees of Freedom of Coincident $f(Q)$-gravity
• Born-Infeld and Charged Black Holes with non-linear source in $f(T)$ Gravity
• Black-Bounce in $f(T)$ Gravity
• Pseudoinvariance and the extra degree of freedom in f(T) gravity
• Non-minimal Coupling of Torsion-matter Satisfying Null Energy Condition for Wormhole Solutions
• Post-Newtonian limit of generalized scalar-torsion theories of gravity
• Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
• Noether Gauge Symmetry of Modified Teleparallel Gravity Minimally Coupled with a Canonical Scalar Field
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Primordial black holes and gravitational waves in teleparallel Gravity
• Lorentz symmetries and primary constraints in covariant teleparallel gravity
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• Boson stars in $f(T)$ extended theory of gravity
• Periodical orbits and waveforms with spontaneous Lorentz symmetry-breaking in Kalb-Ramond gravity
• Disformal transformations in modified teleparallel gravity
• Inflation with F(T) Teleparallel Gravity
• Stability of symmetric teleparallel scalar-tensor cosmologies with alternative connections
• $f(T)$ cosmology: From Pseudo-Bang to Pseudo-Rip
• Scalar induced gravitational waves in metric teleparallel gravity with the Nieh-Yan term
• Scalar induced gravitational waves in symmetric teleparallel gravity with a parity-violating term
• A viable form of the metric Teleparallel F(T) theory of gravity
• Dynamic properties of cyclic cosmologies
• Thick string-like braneworlds in f(T) gravity
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• Revisiting Stability in New General Relativity
• Hamilton's equations in the covariant teleparallel equivalent of general relativity
• On the degrees of freedom count on singular phase space submanifolds
• Towards a possible solution for the coincidence problem: f(G) gravity as background
• Cosmological perturbations in gravitational energy-momentum complex
• Teleparallel bigravity
• Hamiltonian Analysis In New General Relativity
• The issue of Branched Hamiltonian in F(T) Teleparallel Gravity
• Teleparallel gravity: Effects of torsion in 6D braneworlds
• Teleparallel Geometry with Spherical Symmetry: The diagonal and proper frames
• Degrees of Freedom in modified Teleparallel Gravity
• Energy-momentum squared symmetric Teleparallel gravity: $f(Q,T_{\mu \nu }{T}^{\mu \nu })$ gravity
• $f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom
• Reconstructing modified and alternative theories of gravity
• Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on a Proper Frame
• Linear Perturbations and Stability Analysis in $f(T)$ Braneworld Scenario
• First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory
• Hamiltonian analysis of metric-affine-$R^2$ theory
• The Hamiltonian constraint in the symmetric teleparallel equivalent of general relativity
• Role of the remnant symmetries in gravitational theories based on absolute parallelism: a 2D standpoint
• Weak Gravity Limit in Newer General Relativity
• Geometry of teleparallel theories
• Degrees of Freedom of New General Relativity I: Type 2, Type 3, Type 5, and Type 8
• The general expression for $f(T)$ in a charged cylindrical spacetime with diverse dimensions
• Global portraits of nonminimal teleparallel inflation
• Degrees of freedom of a quadratic scalar-nonmetricity theory
• More on Bianchi I spacetimes and f(T) gravity