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

TL;DR

This paper constrains $f(T)$ modified gravity theories by using observational limits on the variation of the gravitational constant, significantly narrowing the allowed parameter space and improving previous constraints.

Contribution

It provides tighter observational constraints on $f(T)$ theories by analyzing the variation of the gravitational constant, reducing the parameter range around zero.

Findings

Allowed model parameters $n$ or $eta$ are tightly constrained near zero.

Constraints on $f(T)$ theories are improved by an order of magnitude.

Results reinforce the viability limits of $f(T)$ models based on gravitational constant variation.

Abstract

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.