Abstract
Modified gravity which was constructed by torsion scalar \(T\), namely \(f(T)\) doesn’t respect Lorentz symmetry. As an attempt to make a new torsion based modified gravity with Lorentz invariance, recently \(f(T,\mathcal{B})\) introduced where \(B=2\nabla_{\mu}T^{\mu}\) (Bahamonde et al. in arXiv:1508.05120, 2015). We would argue, even when theory is constructed and done in a self-consistent form, but if we handle them properly, we observe that there is no Lorentz invariant teleparallel equivalent of \(f(R)\) gravity. All we found is that the \(f(R)\) gravity in which \(R\) must be computed in Weitzenböck spacetime, using Weitzenböck’s connection, nor Levi-Civita connections is the only possible Lorentz invariant type of modified gravity. Consequently, \(f(T)\) gravity can not obey Lorentz symmetry not only in its orthodoxica form but even in this new framework \(f(T,\mathcal{B})\).
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Momeni, D., Myrzakulov, R. On existence of a possible Lorentz invariant modified gravity in Weitzenböck spacetime. Astrophys Space Sci 360, 28 (2015). https://doi.org/10.1007/s10509-015-2546-6
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DOI: https://doi.org/10.1007/s10509-015-2546-6