On validity of the quasi-static approximation in scalar-tensor theories

The discovery of cosmic acceleration motivated extensive studies dynamical dark energy and modified gravity models. Of particular interest are the scalar-tensor theories, with a scalar field non-minimally coupled to matter. Cosmological constraints on these models often employ quasi-static approximation (QSA), in which dynamics perturbations is proportional perturbation matter density. Using QSA simplifies physical interpretation phenomenology results substantial savings computing time when deriving parameter constraints. Focusing symmetron model, well-motivated theory screening mechanism, we compare exact solution linearly perturbed equations those obtained under identify range model parameters for valid. We find that evolution background most important, namely, whether it dominated by Hubble friction or potential. This helps us derive criterion but same argument can be applied other theories generalized Brans-Dicke type. consider two scenarios, one where only couples all