Generalizations of teleparallel gravity and local Lorentz symmetry

Abstract

We analyze the relation between teleparallelism and local Lorentz invariance. We show that generic modifications of the teleparallel equivalent to general relativity will not respect local Lorentz symmetry. We clarify the reasons for this and explain why the situation is different in general relativity. We give a prescription for constructing teleparallel equivalents for known theories. We also explicitly consider a recently proposed class of generalized teleparallel theories, called f(T) theories of gravity, and show why restoring local Lorentz symmetry in such theories cannot lead to sensible dynamics, even if one gives up teleparallelism.

6 pages; v2: minor edits to match published version

References in corpus (15)

• f(R) Theories Of Gravity
• Dark torsion as the cosmic speed-up
• Einstein's Other Gravity and the Acceleration of the Universe
• f(T) Gravity and local Lorentz invariance
• Equation of state for dark energy in $f(T)$ gravity
• Cosmological perturbations in f(T) gravity
• Extended Gravity Theories and the Einstein-Hilbert Action
• Observational constraints on $f(T)$ theory
• Large-scale Structure in f(T) Gravity
• $f(T)$ models with phantom divide line crossing
• The dynamical behavior of $f(T)$ theory
• Growth factor in f(T) gravity
• Observational information for f(T) theories and Dark Torsion
• Conformal transformation in $f(T)$ theories
• Cosmological evolution in exponential gravity

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• $f(T)$ Cosmology with Nonzero Curvature
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