On existence of a possible Lorentz invariant modified gravity in Weitzenböck spacetime

  • Davood MomeniEmail author
  • Ratbay Myrzakulov


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 \(f(T,\mathcal{B})\).


Weitzenböck spacetime Teleparallelism Lorentz symmetry Modified gravity 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Eurasian International Center for Theoretical Physics and Department of General & Theoretical PhysicsEurasian National UniversityAstanaKazakhstan

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