The effective field theory approach to the strong coupling issue in $f(T)$ gravity with a non-minimally coupled scalar field

TL;DR

This paper investigates the strong coupling problem in $f(T)$ gravity by introducing a non-minimally coupled scalar field and employing an effective field theory approach to analyze linear perturbations and potential resolutions.

Contribution

It develops a torsional EFT framework with additional scalar coupling to address the strong coupling issue in $f(T)$ gravity.

Findings

Coupling terms are necessary to avoid degenerate scalar degrees of freedom.

Linear perturbation analysis shows the potential for scalar DoF to propagate.

Revisiting the strong coupling problem in light of scalar propagation is needed.

Abstract

The Hamiltonian analysis for $f(T)$ gravity implies the existence of at least one scalar-type degree of freedom (DoF). However, this scalar DoF of $f(T)$ gravity does not manifest in linear perturbations around a cosmological background, which indicates an underlying strong coupling problem. In this work we expand the scope by introducing an extra scalar field non-minimally coupled to $f(T)$ gravity, aiming to address or alleviate the aforementioned strong coupling problem. Employing the effective field theory (EFT) approach, we provide a class of torsional EFT forms up to second order operators, avoiding the Ostrogradsky ghost. To illustrate this phenomenon, we study a simple model and perform a detailed analysis of its linear scalar perturbations. The results demonstrate that the coupling terms in this toy model are necessary to avoid the initial degenerate situation. The complete avoidance of new constraints requires more coupling terms. Once this vanishing scalar DoF starts propagating in cosmological background at linear level, this phenomenon will demand a revisit of the strong coupling issue that arises in $f(T)$ gravity, particularly in the presence of matter coupling.