Gauge Structure of Teleparallel Gravity

Abstract

During the conference "Teleparallel Universes in Salamanca", we became aware of a recent paper [M. Fontanini, E. Huguet, and M. Le Delliou, Phys. Rev. D 99 (2019) 064006] in which some criticisms on the interpretation of teleparallel gravity as a gauge theory for the translation group were put forward. This triggered a discussion about the arguments on which those criticisms were based, whose output is described in the present paper. The main conclusion is that, to a great extent, those arguments are incorrect, and lack mathematical and physical support.

8 pages. Contribution to the proceedings of the workshop "Teleparallel Universes in Salamanca", Salamanca, Spain, 26-28 November 2018

References in corpus (6)

• Metric-affine approach to teleparallel gravity
• Regularizing role of teleparallelism
• Spin Connection and Renormalization of Teleparallel Action
• Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection?
• Premetric teleparallel theory of gravity and its local and linear constitutive law
• Hodge Dual for Soldered Bundles

Cited by in corpus (43)

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• Local symmetries and physical degrees of freedom in $f(T)$ gravity: a Dirac Hamiltonian constraint analysis
• Cosmological dynamics of dark energy in scalar-torsion $f(T,\varphi )$ gravity
• Dynamical systems analysis in $f(T,\varphi )$ gravity
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Reconstructing inflation in scalar-torsion $f(T,\varphi )$ gravity
• Transit cosmological models with observational constraints in f(Q, T) gravity
• Connection independent formulation of general relativity
• Stability of scalar perturbations in scalar-torsion $f(T,\varphi )$ gravity theories in the presence of a matter fluid
• Generating primordial fluctuations from modified teleparallel gravity with local Lorentz-symmetry breaking
• Attractor behaviour of $f(T)$ modified gravity and the cosmic acceleration
• Slow-roll inflation in generalized scalar-torsion gravity
• The General Linear Cartan Khronon
• Primordial black holes and gravitational waves in teleparallel Gravity
• Scalar induced gravitational waves in modified teleparallel gravity theories
• Spontaneous Scalarization of Black Holes in Gauss-Bonnet Teleparallel Gravity
• Thick accretion disk configurations in the Born-Infeld teleparallel gravity
• $f(Q,L_m)$ gravity, and its cosmological implications
• General relativity as a special case of Poincaré gauge gravity
• Teleparallel theory as a gauge theory of translations: comments and issues
• Inflation and Primordial Fluctuations in $F(T)$ Gravity's Rainbow
• Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation
• Cosmological singularities in $f(T,\varphi )$ gravity
• Quantum fields in teleparallel gravity: renormalization at one-loop
• Constrained transit cosmological models in $f(R,L_m,T)$-gravity
• Dynamics of dark energy in a scalar-vector-torsion theory
• Teleparallel gravity as a gauge theory: coupling to matter with Cartan connection
• Dynamical system analysis in modified Galileon cosmology
• Phase-space analysis of torsion-coupled dilatonic ghost condensate
• From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology
• Cosmological Dynamics in Interacting Scalar-Torsion f(T,$\varphi$) Gravity: Investigating Energy and Momentum Couplings
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• Cartan approach to Teleparallel Equivalent to General Relativity: a review
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• Tangent space symmetries in general relativity and teleparallelism
• Focusing conditions for extended teleparallel gravity theories
• An Improved Framework for Quantum Gravity
• Conservation laws in gauge gravity theory
• Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity
• Towards a unified theory of the fundamental physical interactions based on the underlying geometric structure of the tangent bundle