Topological Casimir effect in models with helical compact dimensions

TL;DR

This paper studies how helical compactification of spatial dimensions affects the vacuum properties of a charged scalar field in curved spacetime, revealing unique effects like nonzero off-diagonal energy-momentum components.

Contribution

It introduces a method to analyze topological effects in helical compactifications, including explicit calculations in de Sitter space with novel vacuum expectation values.

Findings

Helical compactification modifies vacuum expectation values.

Nonzero off-diagonal components appear in the energy-momentum tensor.

Explicit asymptotic behaviors are derived for cosmological expansion.

Abstract

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.