Lowering the strong coupling mode of modified teleparallel gravity theories

We investigate the strong coupling problem in modified teleparallel gravity theories using the effective field theory (EFT) approach, demonstrating that it is possible to shift the emergence of new degrees of freedom (DoFs) to lower orders in perturbation theory. We first focus on the case of $f(T)$ gravity, and we show that in its conformally equivalent form the scalar perturbations are non-dynamical up to the cubic action. We then propose a simple modification of the theory, which lowers the appearance of new DoFs to cubic order, compared to the quartic order in standard $f(T)$ gravity. Our work opens a new avenue to address the issue of strong coupling in modified teleparallel gravity, and suggests a new classification scheme of these theories based on the perturbative order at which new DoFs appear.