Braneworlds in bumblebee gravity

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 $\xi$, between the bumblebee field and gravity shifts the field from the vacuum expectation value. On the other hand, the aether parameter, $\beta$, is responsible for modifying the solution inside the brane.