Fermionic vacuum densities in higher-dimensional de Sitter spacetime

TL;DR

This paper analyzes fermionic vacuum densities in higher-dimensional de Sitter spacetime with compactified dimensions, deriving formulas and studying their behavior during cosmological expansion, highlighting differences from four-dimensional cases.

Contribution

It provides closed-form expressions for fermionic vacuum densities in odd-dimensional de Sitter spacetime and explores their asymptotic behaviors with respect to mass and topology.

Findings

Vacuum densities are exponentially suppressed for large fermion masses.

Topological parts dominate in the early universe when compact dimensions are small.

Oscillatory damping occurs in the topological parts for massive fields at late times.

Abstract

Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for twisted and untwisted massive spinor fields in higher-dimensional de Sitter spacetime with toroidally compactified spatial dimensions. The expectation values are presented in the form of the sum of corresponding quantities in the uncompactified de Sitter spacetime and the parts induced by non-trivial topology. The latter are finite and the renormalization is needed for the first parts only. Closed formulae are derived for the renormalized fermionic vacuum densities in uncompactified odd-dimensional de Sitter spacetimes. It is shown that, unlike to the case of 4-dimensional spacetime, for large values of the mass, these densities are suppressed exponentially. Asymptotic behavior of the topological parts in the expectation values is investigated in the early and late stages of the cosmological expansion. When the comoving lengths of compactified dimensions are much smaller than the de Sitter curvature radius, to the leading order the topological parts coincide with the corresponding quantities for a massless fermionic field and are conformally related to the corresponding flat spacetime results. In this limit the topological parts dominate 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 parts is damping oscillatory.