Fermionic Casimir effect in de Sitter spacetime

TL;DR

This paper analyzes the fermionic Casimir effect in de Sitter spacetime with compactified dimensions, revealing how topology influences vacuum energy and its asymptotic behavior during cosmological expansion.

Contribution

It provides a detailed calculation of the vacuum energy-momentum tensor for a massive spinor field in de Sitter space with arbitrary compactification, including asymptotic behaviors.

Findings

Topological part dominates in the early universe when compactified lengths are small.

In the late universe, the topological contribution exhibits damping oscillations for massive fields.

Conformal relation holds for small compactification scales, linking to flat spacetime results.

Abstract

The Casimir densities are investigated for a massive spinor field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The vacuum expectation value of the energy-momentum tensor is presented in the form of the sum of corresponding quantity in the uncompactified de Sitter spacetime and the part induced by the non-trivial topology. The latter is finite and the renormalization is needed for the first part only. The asymptotic behavior of the topological term is investigated in the early and late stages of the cosmological expansion. When the comoving lengths of the compactified dimensions are much smaller than the de Sitter curvature radius, to the leading order the topological part coincides with the corresponding quantity for a massless fermionic field and is conformally related to the corresponding flat spacetime result with the same topology. In this limit the topological term dominates the uncompactified de Sitter part and the back-reaction effects should be taken into account. In the opposite limit, for a massive field the asymptotic behavior of the topological part is damping oscillatory.