Cenários de mundo-brana em gravitação teleparalela: uma abordagem com invariante de Gauss-Bonnet

Abstract

The present dissertation investigates an alternative gravity model that integrates the teleparallel formulation with Gauss-Bonnet invariant corrections within brane-world scenarios. The work is motivated by the fact that phenomena such as dark energy, cosmological inflation, and the hierarchy problem challenge the Standard Model and General Relativity. It begins with a brief review of General Relativity. Subsequently, the three theoretical pillars of the model are discussed. The first pillar is Teleparallel Gravity. Next, the Gauss-Bonnet term and its teleparallel counterpart are examined. Finally, the addition of an extra dimension via the Randall-Sundrum model is addressed. Methodologically, the reduced action formalism is adopted with a tetrad ansatz compatible with the warped metric. To this end, it is necessary to introduce a lapse function for the extra dimension in order to ensure the appropriate number of equations of motion. From this configuration, the field equations are derived for the general action F(T,GT ), where T is the torsion scalar and GT is the teleparallel equivalent of the Gauss- Bonnet term. The analysis of the model's dynamics reveals that the algebraic complexity of the field equations leads to several consequences, such as the emergence of dynamic for these newlapse function. The study delves into the quadratic case (α GT + βG_T^2). In the thin-brane limit, constraints on the model's parameters are established, demonstrating that the bulk cosmological constant naturally emerges from the geometric corrections. For thick branes, two exact and original solutions were constructed: one kink-like and other 2-kink-like solution. These solutions indicate that the first and second-order Gauss-Bonnet corrections may either interact in a mutually compensating manner, approaching the usual case, or acting together to generate more complex structures, analogous to those produced by multiple scalar fields.