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f(T) Gravity and local Lorentz invariance
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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.
Forward citations
Cited by 2 Pith papers
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$f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom
By perturbing f(T) gravity around FLRW and Bianchi I spacetimes, the authors find that only the two gravitational-wave polarizations propagate in the gravity sector.
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Quasinormal Modes and Dynamical Evolution of Scalar Fields in the Einstein-Bumblebee Theory with a Cosmological Constant
For scalar perturbations of Einstein-Bumblebee black holes in de Sitter spacetime, increasing the Lorentz-violation parameter or the cosmological constant generally lowers the quasinormal mode frequency and damping rate.
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