Probing gravity with relativistic effects

Abstract: Theoretical approaches to large-scale structure strongly depend on the physical regimes considered. On large scales, relativistic effects become important as the standard Newtonian description breaks down. Moreover, these relativistic effects could open a new window for probing the nature of gravity. In this talk, I first show how relativistic galaxy number counts can provide a null test of the weak equivalence principle (EP), and how we can constrain the EP with upcoming Stage-IV surveys in a model-independent way. I then extend this framework to include viscous dark matter, EP violation, and modified gravity, to study whether the EP can still be tested in this context. Interestingly, forecasts for DESI, Euclid, and SKA Phase 2 show that the dark matter viscosity can be constrained at the order of 10^{-6} or better by all three surveys, without assuming the shape of the power spectrum, background evolution, or galaxy bias.