Title: Disentangling modified gravity from a dark force with gravitational redshift

Abstract: The standard approach to test for deviations from General Relativity on cosmological scales is to combine measurements of the growth rate of structure with gravitational lensing. In this study, we show that this method suffers from an important limitation with regard to these two probes: models of dark matter with additional interactions can lead to the very same observational signatures found in modified gravity (and viceversa). Using synthetic data of redshift-space distortions, weak lensing, and cosmic microwave background, we demonstrate that this degeneracy is inevitable between modifications of gravity and a dark fifth force. We then show that the coming generation of surveys, in particular the Square Kilometer Array, will allow us to break the degeneracy between such models through measurements of gravitational redshift. Performing a Markov Chain Monte Carlo analysis of the synthetic data set, we quantify the extent to which gravitational redshift can distinguish between two representative classes of models, Generalized Brans-Dicke (modified gravity) and Coupled Quintessence (fifth force).