Teorias modificadas da gravidade: violação de Lorentz e gravidade cúbica - Lessa, Leandro Alcântara (2024)
In this thesis, we comprehensively explore models and theories aimed at extending the best-known theory for gravity: General Relativity. In the first part of this thesis, we begin with a comprehensive review, explaining the theoretical and experimental motivations that led to the acceptance of Einstein's General Relativity as the most suitable theory to describe gravitational interaction. We showcase its experimental successes but also highlight its limitations. It is precisely in this incompleteness that modified gravity models have been gaining prominence in the current literature. We present the main models of modified gravity, as well as their advantages and disadvantages. In the second part, we explore a specific way to extend General Relativity: the addition of new fields. In this case, we adopt the Lorentz symmetry violation scenario. In this context, we introduce a new perspective on gravitation by adding to the pure gravitational sector described by the Einstein-Hilbert action a new vector field. Due to its dynamics generating preferential directions in spacetime, this field spontaneously breaks the most important local symmetry of General Relativity: Lorentz symmetry. As an application of this new framework, we explore, in diferente geometries, the effects of excitations of the vector field of self-interaction known as the Bumblebee. In the third part, we modify Einstein's theory by adding new invariants to the usual gravitational action, i.e., to the Ricci scalar. In this case, we detail the main models in the literature that introduce these new invariants, highlighting their successes and limitations. In the end, we present our main results through two applications, based on cubic gravity theory. This high-curvature theory is constructed through invariants formed with three curvature tensors. Different cubic gravities were addressed, such as the so-called Einsteinian Cubic Gravity, which served as the basis for our first application with black hole solutions, where the source is given by nonlinear electrodynamics. To conclude the thesis, we construct a high-curvature theory with up to cubic interaction in the context of braneworlds.