Relativistic scalar fields and the quasistatic approximation in theories of modified gravity

Relativistic scalar fields are ubiquitous in modified theories of gravity. An important tool in understanding their on structure formation, especially in the context of N-body simulations, is the quasistatic approximation in which the time evolution of perturbations in the scalar fields is discarded. We show that this approximation must be used with some care by studying linearly perturbed scalar field cosmologies and quantifying the errors that arise from taking the quasistatic limit. We focus on f(R) and chameleon models and link the accuracy of the quasistatic approximation to the fast/slow-roll behavior of the background and its proximity to ΛCDM. Investigating a large range of scales, from super- to subhorizon, we find that slow-rolling (ΛCDM-like) backgrounds generically result in good quasistatic behavior, even on (super-)horizon scales. We also discuss how the approximation might affect studying the nonlinear growth of structure in numerical N-body simulations.