f(T) Gravity and local Lorentz invariance

Abstract

We show that in theories of generalised teleparallel gravity, whose Lagrangians are algebraic functions of the usual teleparallel Lagrangian, the action and the field equations are not invariant under local Lorentz transformations. We also argue that these theories appear to have extra degrees of freedom with respect to general relativity. The usual teleparallel Lagrangian, which has been extensively studied and leads to a theory dynamically equivalent to general relativity, is an exception. Both of these facts appear to have been overlooked in the recent literature on f(T) gravity, but are crucial for assessing the viability of these theories as alternative explanations for the acceleration of the universe.

4 pages, no figure; v2: Added discussion about modifying the theory in order to make it manifestly Lorentz covariant and one reference; v3: minor changes to match published version

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Cited by in corpus (299)

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• The covariant formulation of f(T) gravity
• Modified teleparallel theories of gravity
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• Cosmography in f(T)-gravity
• Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics
• New Horizons for Fundamental Physics with LISA
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• Non trivial frames for f(T) theories of gravity and beyond
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• Growth factor in f(T) gravity
• Spherically symmetric static spacetimes in vacuum f(T) gravity
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• On the covariance of teleparallel gravity theories
• Conformal symmetry and accelerating cosmology in teleparallel gravity
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• Static Anisotropic Solutions in f(T) Theory
• Anisotropic Universe Models in f(T) Gravity
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• F(T) Models within Bianchi Type I Universe
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• Bouncing Loop Quantum Cosmology from $F(T)$ gravity
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• Dynamical systems approach and generic properties of $f(T)$ cosmology
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• Conformal transformations in modified teleparallel theories of gravity revisited
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• Modified gravity: a unified approach
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• Analytic rotating black hole solutions in $N$-dimensional $f(T)$ gravity
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• Toward a concordance teleparallel Cosmology I: Background Dynamics
• Logamediate Inflation in f(T) Teleparallel Gravity
• Stability of scalar perturbations in scalar-torsion $f(T,\varphi )$ gravity theories in the presence of a matter fluid
• Connection independent formulation of general relativity
• Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term
• McVittie solution in f(T) gravity
• Density Perturbation Growth in Teleparallel Cosmology
• Spontaneous Lorentz symmetry-breaking constraints in Kalb-Ramond gravity
• Thermodynamic properties of modified gravity theories
• Generating primordial fluctuations from modified teleparallel gravity with local Lorentz-symmetry breaking
• Post-Newtonian Approximation of Teleparallel Gravity Coupled with a Scalar Field
• Matter stability in modified teleparallel gravity
• Thermodynamics of the viscous $f(T,B)$ gravity in the new agegraphic dark energy model
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• Black-Bounce in $f(T)$ Gravity
• Generalised nonminimally gravity-matter coupled theory
• Role of spacetime boundaries in Einstein's other gravity
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• Cosmological models in $f(T,\mathcal{T})$ gravity and the dynamical system analysis
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• Fermion localization in braneworld teleparallel f(T,B) gravity
• Inhomogeneous Universe in f(T) Theory
• Planar Symmetry in f(T) gravity
• Growth of matter overdensities in non-minimal torsion-matter coupling theories
• Symmetron and de Sitter attractor in a teleparallel model of cosmology
• Lorenz Gauge Fixing of $f(T)$ Teleparallel Cosmology
• On Kasner solution in Bianchi I $f(T)$ cosmology
• Limiting curvature mimetic gravity and its relation to Loop Quantum Cosmology
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• Spherical Accretion of Matter by Charged Black Holes on f(T) Gravity
• Scalar induced gravitational waves in modified teleparallel gravity theories
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• Cosmic evolution in f(T) gravity theory
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• Solar system tests for realistic $f(T)$ models with nonminimal torsion-matter coupling
• Reconstructions of $f(T)$ Gravity from Entropy Corrected Holographic and New Agegraphic Dark Energy Models in Power-law and Logarithmic Versions
• On spherically symmetric vacuum solutions and horizons in covariant $f(T)$ gravity theory
• Inflation with F(T) Teleparallel Gravity
• Accelerating Cosmological Models in $f(T,B)$ Gravitational Theory
• Evaporation phenomena in f(T) gravity
• Geodesic Deviation Equation in $\Lambda$CDM $f(T,\mathcal{T})$ gravity
• Bouncing solutions in $f(T)$ gravity
• Junction Conditions for F(T) Gravity from a Variational Principle
• Unexplored regions in teleparallel $f(T)$ gravity: Sign-changing dark energy density
• $f(T)$ non-linear massive gravity and the cosmic acceleration
• Bouncing cosmologies via modified gravity in the ADM formalism: Application to Loop Quantum Cosmology
• The Hidden Flat Like Universe II: Quasi inverse power law inflation by $f(T)$ gravity
• Noether symmetry in a nonlocal f(T) Gravity
• Teleparallel Equivalent of Lovelock Gravity, Generalizations and Cosmological Applications
• Phase Space description of Nonlocal Teleparallel Gravity
• Birkhoff's Theorem in f(T) Gravity up to the Perturbative Order
• Charged Anti-de Sitter BTZ black holes in Maxwell-$f(T)$ gravity
• Rotating charged AdS solutions in quadratic $f(T)$ gravity
• Towards realistic $f(T)$ models with nonminimal torsion-matter coupling extension
• Generic Phase Portrait Analysis of the Finite-time Singularities and Generalized Teleparallel Gravity
• Regularization of $f(T)$ gravity theories and local Lorentz transformation
• Configurational Entropy and braneworlds in f(T,B) gravity
• Transient acceleration in $f(T)$ gravity
• Inflation and Primordial Fluctuations in $F(T)$ Gravity's Rainbow
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• $f(T)$ Cosmology with Nonzero Curvature
• Dynamic properties of cyclic cosmologies
• Charged gravastar model in $f(T)$ gravity admitting conformal motion
• A geometric view on local Lorentz transformations in teleparallel gravity
• Note on the charged boson stars with torsion-coupled field
• A viable form of the metric Teleparallel F(T) theory of gravity
• On existence of a possible Lorentz invariant modified gravity in Weitzenböck spacetime
• Anisotropic cosmological dynamics in $f(T)$ gravity in the presence of a perfect fluid
• Thick string-like braneworlds in f(T) gravity
• Scale-invariant cosmology in de Sitter gauge theory
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• Variational Problem and Bigravity Nature of Modified Teleparallel Theories
• Bifurcation and Global Dynamical Behavior of the $f(T)$ Theory
• Towards a possible solution for the coincidence problem: f(G) gravity as background
• Bianchi I cosmological solutions in teleparallel gravity
• Spherical collapse and virialization in $f(T)$ gravities
• Regular solutions in $f(T)$-Yang-Mills theory
• New proper tetrad for teleparallel gravities in non-flat spacetime
• Dynamical Instability of Shear-free Collapsing Star in Extended Teleparallel Gravity
• Mimetic f(T) Teleparallel gravity and cosmology
• Dynamical Instability of Cylindrically Symmetric Collapsing Star in Generalized Teleparallel Gravity
• Non-minimally Coupled Tachyon Field in Teleparallel Gravity
• Observational Hubble parameter data constraints on the interactive model of $f(T)$ gravity with particle creation
• Generalized Teleparallel Theory
• Local Lorentz transformation and exact spherically symmetric vacuum solutions in f(T) gravity theories
• Cosmological perturbations in a class of fully covariant modified theories: Application to models with the same background as standard LQC
• Inhomogeneous solutions in $f(T,B)$ gravity
• Note on bouncing backgrounds
• Extended Geometric Trinity of Gravity
• Brane cosmology in teleparallel and $f(T)$ gravity
• Deformed Weitzenböck Connections and Double Field Theory
• Spin connection and cosmological perturbations in $f(T)$ gravity
• Cosmological Dynamics in Interacting Scalar-Torsion f(T,$\varphi$) Gravity: Investigating Energy and Momentum Couplings
• Gravitational energy and radiation of a charged black hole
• A remarkably simple theory of 3d massive gravity
• Realistic f(T) model describing the de Sitter epoch of the dark energy dominated universe
• Teleparallel Geometry with Spherical Symmetry: The diagonal and proper frames
• Interacting Induced Dark Energy Model
• $f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom
• Phenomenological models of Universe with varying $G$ and $\Lambda$
• Higher-Curvature Gravity, Black Holes and Holography
• Teleparallel geometries not characterized by their scalar polynomial torsion invariants
• Probing symmetric teleparallel gravity in the early universe
• The meaning of torsion in teleparallel theories
• Cosmological Issues in $F(T)$ Gravity Theory
• Spin connection and cosmological perturbations in scalar-torsion gravity
• First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory
• Action functional of the Cardassian universe
• Vulnerability of f(Q) gravity theory and a possible resolution
• Linear Perturbations and Stability Analysis in $f(T)$ Braneworld Scenario
• Phase space structure of symmetric teleparallel theory of gravity
• Definition of Good Tetrads for f(T) Gravity
• Generalized Hidden Conformal Symmetry in Quadratic $f(T)$ Gravity
• Matter Creation Cosmologies and Accelerated Expansion
• Classical and quantum cosmology in $f(T)$-gravity theory: A Noether symmetry approach
• Unimodular Gravity and Averaging
• Stability of Differentially Rotating Disks in $f(T)$ Theory
• Tensor stability in Born-Infeld determinantal gravity
• Exact Analytical Taub-NUT like Solution in f(T) Gravity
• Deformed Weitzenböck Connections and Teleparallel Gravity
• Teleparallel Poincaré Cosmology and $\Lambda$CDM Model
• Acceleration of the universe in matter dominant era by conformal symmetry breaking
• Issue of Branched Hamiltonian, Inflation and indispensability of scalar field in generalized Teleparallel theories
• Covariant density and velocity perturbations of the quasi-Newtonian cosmological model in $f(T)$ gravity
• Black holes solutions in power-law Maxwell-$f(T)$ gravity in diverse dimensions
• Is torsion needed in a theory of gravity? A reappraisal
• Neutron Stars in Scalar Torsion Theories with Nonminimal Coupling
• Kalb-Ramond field induced cosmological bounce in generalized teleparallel gravity
• Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity