Probing gravity at cosmic scales

The theoretical explanation of cosmic acceleration is nowadays one of the biggest puzzles in cosmology. Within the standard cosmological model (LCDM) the expansion is sourced by the vacuum energy associatedto the Cosmological Constant L. Despite its simplicity, the Cosmological Constant presents various unresolved problems from both the theoretical and the observational side.However, even if we dismiss these puzzles, the study of theoretical alternatives to LCDM is still of primary importance. In fact, the wealth and quality of cosmological data that we are expecting for thenext decade will allow us to test gravity on cosmological scales with unprecedented accuracy. This will give us the chance to investigate many of our theoretical ideas and to assess the strength of the standard model of cosmology on the largest scales.In this thesis we present different approaches that we can adopt to study modifications of gravity by means of cosmology.