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

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.

Galaxy–Galaxy Lensing Data: f(T) Gravity Challenges General Relativity

“…However, one could start from the equivalent formulation of gravity in terms of torsion (Maluf 2013), and follow similar procedures, resulting in f (T) gravity (Cai et al 2016;Krssak et al 2019;Bahamonde et al 2023), f (T, T G ) gravity (Kofinas & Saridakis 2014), f (T, B) gravity (Bahamonde et al 2015), etc. These classes of theories have been shown to present very interesting phenomenology (Cai et al 2018;Ren et al 2021aRen et al , 2022Hu et al 2023bHu et al , 2023a. Furthermore, one may take into account nonmetricity, and construct symmetric teleparallel gravity and f (Q) gravity (Beltrán Jiménez et al 2018;Anagnostopoulos et al 2021).…”