Gravity beyond general relativity

We introduce the standard model of cosmology based on general relativity and discuss its successes and problems. We then discuss motivations to consider gravitational theories beyond general relativity and summarize observational and theoretical constraints that these theories need to satisfy. A special focus is laid on screening mechanisms, which hide deviations from general relativity in the Solar System and enable large modifications to general relativity on astrophysical and cosmological scales. Finally, several modified gravity models are introduced, which satisfy the Solar System constrains as well as the constraint on the speed of gravitational waves obtained from almost simultaneous detections of gravitational waves and gamma ray bursts from a neutron star merger (GW170817/GRB 170817A).