Deviations from General Relativity in Cosmology and Astrophysics

Two of the most prominent challenges of Modern Cosmology are the recent late-time accelerated expansion of the Universe and Dark Matter (DM). DM is of fundamental importance in the process of structure formation at galactic, extragalactic and cosmic scales. It seems to dominate down to small galactocentric radii, as highlighted by the galaxies rotation curves and on cosmic scale, it is well known that the spatial distribution of galaxies is biased with respect to the underlying DM distribution. This relation is called ``bias''. Part of this thesis is devoted to the investigation of the DM issue. In particular, we study the DM density profile in the Orion dwarf galaxy. This galaxy is a good candidate to understand the physics of DM as in general, the kinematics of dwarf galaxies is dominated by this dark component. Moreover, due to the availability of high precision data, it becomes crucial to understand accurately the bias relation, so we elaborate on the Lagrangian bias, when the initial mass fluctuation field is considered Gaussian and the bias is local. It is well known that the \Lambda CDM has been very successful in accounting for current cosmological data, although it suffers from some outstanding problems, such as the small value of \Lambda, DM problems on small scales, early Universe shortcomings and the lack of a correct scheme to quantize General Relativity. These lead people to propose and investigate alternative models, which are based on deviations from General Relativity at cosmic scales. The bulk of the present thesis is devoted to the study of gravity theories, which consider an extra scalar degree of freedom (DoF), in order to modify the gravitational interaction at large scales and account for the late time acceleration. In particular, we develop the gradient expansion formalism in order to explore the phenomenology associated with the non-linear derivative interactions of the most general scalar tensor theories that lead to second order field equations. This approach is very useful to probe on super horizon scale the Inflation scenario. Finally, in the quest of a model independent parametrization for gravity theories, the effective field theory formalism has been applied to the phenomenon of cosmic acceleration. It is developed using a perturbative approach in which an extra scalar DoF appears only at the level of perturbations. We investigate the viability of background functions by means of a thorough dynamical analysis. In conclusion, we present the implementation of this framework into CAMB/CosmoMC creating, what we dubbed, EFTCAMB/EFTCosmoMC. These codes will allow to test gravity theories with the most recent data releases.