Observational Constraints on $f(T)$ gravity from varying fundamental   constants
  We use observations related to the variation of fundamental constants, in order to impose constraints on the viable and most used $f(T)$ gravity models. In particular, for the fine-structure constant we use direct measurements obtained by different spectrographic methods, while for the effective Newton's constant we use a model-dependent reconstruction, using direct observational Hubble parameter data, in order to investigate its temporal evolution. We consider two $f(T)$ models and we quantify their deviation from $\Lambda$CDM cosmology through a sole parameter. Our analysis reveals that this parameter can be slightly different from its $\Lambda$CDM value, however the best-fit value is very close to the $\Lambda$CDM one. Hence, $f(T)$ gravity is consistent with observations, nevertheless, as every modified gravity, it may exhibit only small deviations from $\Lambda$CDM cosmology, a feature that must be taken into account in any $f(T)$ model-building. 
Rafael C. Nunes, Alexander Bonilla, Supriya Pan, Emmanuel N. Saridakis
gr-qc astro-ph.CO hep-th