Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. Modified gravity theories have richer observational consequences for large-scale structure than conventional dark energy models, in that different observables are not described by a single growth factor. We examine the relationships between perturbations in the metric potentials, density and velocity fields, and discuss strategies for measuring them using gravitational lensing and other probes of large-scale structure. We show how a broad class of gravity theories can be tested by combining these probes.

The possible clustering of dark energy can mimic features of modified gravity theories and thus confuse the search for distinct signatures of such theories if it has pressure perturbations and anisotropic stresses. With these two extra degrees of freedom, we consider the question: can a clustered dark energy model mimic modified gravity models in all observational tests?