$f(T)$ Theories and Varying Fine Structure Constant

In analogy to $f(R)$ theory, recently a new modified gravity theory, namely the so-called $f(T)$ theory, has been proposed to drive the current accelerated expansion without invoking dark energy. In the present work, by extending Bisabr's idea, we try to constrain $f(T)$ theories with the varying fine structure "constant", $α\equiv e^2/\hbar c$. We find that the constraints on $f(T)$ theories from the observational $Δα/α$ data are very severe. In fact, they make $f(T)$ theories almost indistinguishable from $Λ$CDM model.

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