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

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.