Induced Fermionic vacuum polarization in dS spacetime with a compactified cosmic string

TL;DR

This paper investigates how a cosmic string and compactified dimension in de Sitter spacetime affect fermionic vacuum polarization, revealing that the fermionic condensate vanishes for massless fields and providing detailed decompositions of vacuum expectation values.

Contribution

It provides a detailed analysis of fermionic vacuum polarization in dS spacetime with a cosmic string and compactification, including new decompositions of condensates and energy-momentum tensor components.

Findings

Fermionic condensate vanishes for massless fermions.

Vacuum expectation values are decomposed into string-induced and compactification-induced parts.

Results highlight the influence of cosmic strings and compact dimensions on quantum fields in curved spacetime.

Abstract

We study the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy-momentum tensor for a massive spinor field in the de Sitter (dS) spacetime including an ideal cosmic string. In addition, spatial dimension along the string is compactified to a circle of length $L$. The fermionic field is assumed to obey quasi-periodic condition along the $z$-axis. There are also magnetic fluxes running along the cosmic string and enclosed by the compact dimension. Both, the FC and the VEV of the energy-momentum tensor, are decomposed into two parts: one induced by the cosmic string in dS spacetime considering the absence of the compactification, and another one induced by the compactification. In particular, we show that the FC vanishes for a massless fermionic field.