  We investigate the influence of the helical compactification of spatial
dimension on the local properties of the vacuum state for a charged scalar
field with general curvature coupling parameter. A general background geometry
is considered with rotational symmetry in the subspace with the coordinates
appearing in the helical periodicity condition. It is shown that by a
coordinate transformation the problem is reduced to the problem with standard
quasiperiodicity condition in the same local geometry and with the effective
compactification radius determined by the length of the compact dimension and
the helicity parameter. As an application of the general procedure we have
considered locally de Sitter spacetime with a helical compact dimension. By
using the Hadamard function for the Bunch-Davies vacuum state, the vacuum
expectation values of the field squared, current density, and energy-momentum
tensor are studied. The topological contributions are explicitly separated and
their asymptotics are described at early and late stages of cosmological
expansion. An important difference, compared to the problem with quasiperiodic
conditions, is the appearance of the nonzero off-diagonal component of the
energy-momentum tensor and of the component of the current density along the
uncompact dimension.
