Scalar and fermionic vacuum currents in de Sitter spacetime with compact dimensions

Abstract

Vacuum expectation values (VEVs) of the current densities for charged scalar and Dirac spinor fields are investigated in $(D+1)$-dimensional de Sitter (dS) spacetime with toroidally compactified spatial dimensions. Along compact dimensions we impose quasiperiodicity conditions with arbitrary phases. In addition, the presence of a classical constant gauge field is assumed. The VEVs of the charge density and of the components for the current density along noncompact dimensions vanish. The gauge field leads to Aharonov-Bohm-like oscillations of the components along compact dimensions as functions of the magnetic flux. For small values of the comoving length of a compact dimension, compared with the dS curvature scale, the current density is related to the corresponding current in the Minkowski spacetime by a conformal relation. For large values of the comoving length and for a scalar field, depending on the mass of the field, two different regimes are realized with the monotonic and oscillatory damping of the current density. For a massive spinor field, the decay of the current density is always oscillatory. In supersymmetric models on the background of Minkowski spacetime with equal number of scalar and fermionic degrees of freedom and with the same phases in the periodicity conditions, the total current density vanishes due to the cancellation between the scalar and fermionic parts. The background gravitational field modifies the current densities for scalar and fermionic fields in different ways, and for massive fields there is no cancellation in the dS spacetime.