Casimir energy and topological mass for a massive scalar field with Lorentz violation

A Lorentz symmetry violation aether-type theoretical model is considered to investigate the Casimir effect and the generation of topological mass associated with a self-interacting massive scalar fields obeying Dirichlet, Newman and mixed boundary conditions on two large and parallel plates. By adopting the path integral approach we found the effective potential at one- and two-loop corrections which provides both the energy density and topological mass when taken in the ground state of the scalar field. We then analyse how these quantities are affected by the Lorentz symmetry violation and compare the results with previous ones found in literature.