Dynamics of Linear Perturbations in f(R) Gravity

We consider predictions for structure formation from modifications to general relativity in which the Einstein-Hilbert action is replaced by a general function of the Ricci scalar. We work without fixing a gauge, as well as in explicit popular coordinate choices, appropriate for the modification of existing cosmological code. We present the framework in a comprehensive and practical form that can be directly compared to standard perturbation analyses. By considering the full evolution equations, we resolve perceived instabilities previously suggested, and instead find a suppression of perturbations. This result presents significant challenges for agreement with current cosmological structure formation observations. The findings apply to a broad range of forms of $f(R)$ for which the modification becomes important at low curvatures, disfavoring them in comparison with the $\ensuremath{\Lambda}\mathrm{CDM}$ scenario. As such, these results provide a powerful method to rule out a wide class of modified gravity models aimed at providing an alternative explanation to the dark energy problem.