Relatividade geral e gravidade modificada em galáxias e no Sistema Solar - Almeida, Álefe de Oliveira Freire de (2019)
General relativity has a great success in describing the dynamics of the Solar System and also in the description of gravitational waves. However, its limits are evident in the study of large scales and quantum levels. In this latter scenario it is known that general relativity is not perturbatively renormalizable, hence proposed approaches as functional renormalization have been applied in order to solve this problem. However, the use of such mechanisms gives rise to extensions of general relativity that can generate signatures of the quantum medium at larger scales. In this thesis we study a particular extension of general relativity from renormalization group and we test if such signatures are present at scales at the level of the Solar System. In addition, there is a reasonable understanding that general relativity does not explain the behavior of rotation curves without the hypothesis of a dark matter. The fact that galaxies have very low rotation velocities in relation to the speed of light and a weak gravitational field and that, in this regime, general relativity is simply Newtonian gravity, it suggests that general relativity corrections are inefficient for dark matter effects. We study in this thesis alternatives to the interpretation described above and we propose a model that tests them in their own way. In addition, we study the feasibility of a scenario of coexistence between dark matter and modified gravity assuming that the fifth force from the gravity modification is coupled differently to baryons and dark matter. We investigate the possibility that the galaxy rotation curves can be explained in the framework of modified gravity models that introduce a Yukawa term in the gravitational potential. We aim at constraining the modified gravity parameters ß and ?, that is, the strength and the range of the Yukawa fifth force. We include baryonic gas, disk and bulge components, along with a Navarro-Frenk and White (NFW) halo of dark matter. Each galaxy rotation curve is modeled with three free parameters, beside the two global Yukawa parameter. The preference of the observational data in favor or against this new parameterization is studied through Bayesian inference. The Bayesian evidence in favor of a NFW profile plus Yukawa term is higher than 8s with respect to the standard gravity parametrization.