Vacuum densities for a charged scalar field in de Sitter space-time with compact dimensions

Abstract

The vacuum expectation value of the energy-momentum tensor is investigated for a charged scalar field in dS space-time with toroidally compact spatial dimensions in the presence of a classical constant gauge field. Due to the nontrivial topology, the latter gives rise to an Aharonov-Bohm-like effect on the vacuum characteristics. The vacuum energy density and stresses are even periodic functions of the magnetic flux enclosed by the compact dimensions. For small values of the comoving lengths of the compact dimensions as compared with the dS curvature radius, the effects of gravity on the topological contributions are small, and the expectation values are expressed in terms of the corresponding quantities in the Minkowski bulk by the standard conformal relation. For large values of the comoving lengths, depending on the field mass, two regimes are realized with monotonic and oscillatory damping of the expectation values. We show that the sign of the the vacuum energy density can be controlled by tuning the magnetic flux enclosed by the compact dimensions.