Braneworlds in bumblebee gravity

Abstract

We investigate thick-brane solutions within the five-dimensional bumblebee gravity in the presence of a real scalar field. Specifically, we implement the Lorentz symmetry breaking scenario within this context and obtain brane-like structures. Since the contribution of the bumblebee field is expected to be weak, we solve the field equations in the small-parameter regime. In this situation, we develop a first-order framework to describe the brane. The results show that the function which drives the bumblebee field may engender a lumplike structure whose shape depends on the parameters. On one hand, the effect of the non-minimal coupling, controlled by ξ, between the bumblebee field and gravity shifts the field from the vacuum expectation value. On the other hand, the aether parameter, β, is responsible for modifying the solution inside the brane.