Narrow Results

One of the challenges in connecting higher dimensional theories to cosmology is stabilization of the moduli fields. We investigate the role of a Lorentz violating vector field in the context of stabilization. Specifically, we compute the one-loop Casimir energy in Randall–Sundrum five-dimensional (non-supersymmetric) S¹/ Z₂ orbifolds resulting from the interaction of a real scalar field with periodic boundary conditions with a Lorentz violating vector field. We find that the result is an enhanced attractive Casimir force. Hence, for stability, positive contributions to the Casimir force from branes and additional fields would be required to counter the destabilizing, attractive effect of Lorentz violating fields.

In this paper, we consider a Lorentz-breaking scalar field theory within the Horava–Lifshtz approach. We investigate the changes that a space–time anisotropy produces in the Casimir effect. A massless real quantum scalar field is considered in two distinct situations: between two parallel plates and inside a rectangular two-dimensional box. In both cases, we have adopted specific boundary conditions on the field at the boundary. As we shall see, the energy and the Casimir force strongly depends on the parameter associated with the breaking of Lorentz symmetry and also on the boundary conditions.