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 β has been significantly shrunk to a very narrow range around zero. In fact, the results improve the previous constraints by an order of magnitude.