The effective field theory approach to the strong coupling issue in f(T) gravity

We investigate the scalar perturbations and the possible strong coupling issues of f(T) around a cosmological background, applying the effective field theory (EFT) approach. We revisit the generalized EFT framework of modified teleparallel gravity, and apply it by considering both linear and second-order perturbations for f(T) theory. We find that no new scalar mode is present in both linear and second-order perturbations in f(T) gravity, which suggests a strong coupling problem. However, based on the ratio of cubic to quadratic Lagrangians, we provide a simple estimation of the strong coupling scale, a result which shows that the strong coupling problem can be avoided at least for some modes. In conclusion, perturbation behaviors that at first appear problematic may not inevitably lead to a strong coupling problem, as long as the relevant scale is comparable with the cutoff scale M of the applicability of the theory.