This thesis investigates new cosmological information that can be obtained from present and future large-scale galaxy surveys, in order to constrain our theory of gravity. We introduce directly observable cosmological probes and discuss model independent measurements, useful to put complementary constraints on cosmological parameters. We compute, through cosmological perturbation theory, fully relativistic expressions describing the galaxy distribution in the Universe. All relevant observational effects are included, and a code is provided for fast and accurate numerical evaluations. We forecast the capability of future experiments to constrain sub-leading terms contributing to the galaxy spectrum and bi-spectrum. New promising probes are associated in particular with the weak lensing effect on galaxy statistical distributions, which represents an alternative constraint on the lensing potential, therefore on our gravity theory.