Upcoming galaxy surveys are aiming to map the largest scales of our observable universe in the next decades. With these data we can test gravity on scales near the horizon by studying the signatures of modified gravity models on large scale structure observables.
I will present the imprints on the galaxy number counts (GNC's) and on the cross-correlation of the GNC's with CMB temperature anisotropies from certain classes of scalar-tensor theories of gravity embedded in the Horndeski Lagrangian. Furthermore fundamental properties of gravity, e.g. the propagation speed of tensor perturbations, can be tested using an effective field theory approach.
Due to the remarkable modifications of relativistic effects which contribute to the considered signals, like the integrated Sachs-Wolfe effect, these observables allow us to constrain or even rule out some alternative models.