Facets of gravity

Starting from the defining key properties of General Relativity, I will explain in which consistent ways these properties can be modified. Within the geometrical interpretation of gravity this will allow me to introduce more general space-time geometries and I will illustrate simpler formulations of General Relativity as well as modifications based on affine structure. In the field theory perspective I will discuss the building blocks of modifications based on additional degrees of freedom in the gravity sector (like massive gravity, the Horndeski scalar-tensor theories). In this context I will focus on constructing consistent vector-tensor theories, the so called generalized Proca theories and discuss some of their immediate consequences.