Constraining $f(T)$ Theories with the Varying Gravitational Constant

As is well known, a varying effective gravitational “constant” is one of the common features of most modified gravity theories. Of course, as a modified gravity theory, $f(T)$ theory is not an exception. Noting that the observational constraint on the varying gravitational “constant” is very tight, in the present work we try to constrain $f(T)$ theories with the varying gravitational “constant”. We find that the allowed model parameter $n$ or $\beta$ has been significantly shrunk to a very narrow range around zero. In fact, the results improve the previous constraints by an order of magnitude.