Algumas soluções em teorias de gravitação modificada

Abstract

In this work, the causality issues are discussed in a non-Riemannian geometry, called Lyra geometry. It is a non-Riemannian geometry originated from Weyl geometry. In order to compare this geometry with the Riemannian geometry, the Einstein field equations are considered. It is verified that the Gödel and Gödel-type metric are consistent with this non-Riemannian geometry. A non-trivial solution for Gödel universe in the absence of matter sources is determined without analogue in general relativity. Different sources are considered and then different conditions for causal and non-causal solutions are discussed. The Ricci dark energy is a model inspired by the holographic dark energy models with the dark energy density being proportional to Ricci scalar curvature. Here, this model is studied in the bumblebee gravity theory. It is a gravitational theory that exhibit spontaneous Lorentz symmetry breaking. Then, the modified Friedmann equation is solved for two cases. In the first case, the coupling constant ξ is equal to zero and in the second case a solution in the vacuum, where the bumblebee field becomes a constant that minimizes the potential, is considered. The coupling constant controls the interaction gravity-bumblebee. The Gödel-type universe is introduced in the context of bumblebee gravity and then the causality and its violation is studied. Causal and non-causal Gödel-type solutions are obtained for different content of matter. In addition, when the coupling constant is zero, the bumblebee potential may be associated with the value of the cosmological constant of the general relativity. Furthermore, the case with the non-zero coupling constant is also investigated.