Conformal transformation of f(Q) gravity and its cosmological perturbations

TL;DR

This paper explores the conformal transformation of f(Q) gravity within symmetric teleparallel gravity, analyzing its cosmological perturbations and discussing potential issues like strong coupling at the linear level.

Contribution

It provides a detailed study of the conformal scalar-tensor equivalent of f(Q) gravity and examines the behavior of cosmological perturbations, highlighting issues with degrees of freedom and linear perturbation breakdown.

Findings

f(Q) gravity exhibits different degrees of freedom depending on the background.

Linear perturbation theory may break down, indicating potential strong coupling problems.

The conformal transformation approach clarifies the nature of perturbations in f(Q) models.

Abstract

Symmetric teleparallel gravity (STG) is a gravity theory which takes non-metricity tensor to describe gravity effects. In the STG framework, we study the conformal equivalent scalar-tensor theory of f(Q) model and calculate the cosmological linear perturbations of the conformal transformed action. We confirm the result already present in references that f(Q) gravity shows different degrees of freedom on different backgrounds at linear perturbation level. We also explain that this situation often means the linear perturbation theory breaks down and the model may suffer from strong coupling problem.