Gravity beyond General Relativity: New Proposals and their Phenomenology

This Thesis is devoted to the study of phenomenologically viable gravitational theories, in order to address the most pressing open issues both at very small and very large energy scales. Lovelock’s theorem singles out General Relativity as the only theory with secondorder field equations for the metric tensor. So, two possible ways to circumvent it and modify the gravitational sector are taken into account. The first route consists in giving up diffeomorphism invariance, which generically leads to extra propagating degrees of freedom. In this framework Horava gravity is discussed, presenting two restrictions, called respectively "projectability" and "detailed balance", which are imposed in order to reduce the number of terms in the full theory. We introduce a new version of the theory assuming detailed balance but not projectability, and we show that such theory is dynamically consistent as both the spin-0 and spin-2 gravitons have a well behaved dynamics at low-energy. Moreover three-dimensional rotating black hole solutions are found and fully studied in the context of Horava gravity, shedding light on its causal structure. A new concept of black hole horizon, dubbed "universal horizon", arises besides the usual event horizon one, since in Lorentz-violating gravity theories there can be modes propagating even at infinite speed. The second route which is considered, consists in adding extra fields to the gravitational action while diffeomorphism invariance is preserved. In this respect we consider the less explored option that such fields are auxiliary fields, so they do not satisfy dynamical equations but can be instead algebraically eliminated. A very general parametrization for these theories is constructed, rendering also possible to put on them very tight, theory-independent constraints. Some insight about the cosmological implications of such theories is also given. Finally in the conclusions we discuss about the future challenges that the aforementioned gravity theories have to face.