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

TL;DR

This paper uses the effective field theory approach to analyze scalar perturbations in $f(T)$ gravity, finding that potential strong coupling issues can be mitigated depending on the relevant energy scale.

Contribution

It applies the EFT framework to $f(T)$ gravity at both linear and second order, providing a new estimation of the strong coupling scale and conditions to avoid it.

Findings

No new scalar mode in perturbations suggests potential strong coupling issues.

The strong coupling scale can be sufficiently high to avoid problems for some modes.

Perturbation behavior may not imply unavoidable strong coupling if the relevant scale is near the cutoff.

Abstract

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. No new scalar mode is present in 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.