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

TL;DR

This paper investigates $f(T)$ modified gravity theories by analyzing how they affect the variation of the fine structure constant, finding observational constraints that limit their deviation from the standard $\Lambda$CDM model.

Contribution

It extends previous ideas to constrain $f(T)$ theories using observational data on the fine structure constant's variation, showing these theories are tightly limited by current measurements.

Findings

Constraints from $\Delta\alpha/\alpha$ data are very strict.

$f(T)$ theories are nearly indistinguishable from $\Lambda$CDM.

Observational data significantly limit deviations in $f(T)$ models.

Abstract

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", $\alpha\equiv e^2/\hbar c$. We find that the constraints on $f(T)$ theories from the observational $\Delta\alpha/\alpha$ data are very severe. In fact, they make $f(T)$ theories almost indistinguishable from $\Lambda$CDM model.