Fermionic vacuum polarization by a cosmic string in de Sitter spacetime

TL;DR

This paper studies how a cosmic string affects fermionic quantum fields in de Sitter space, revealing unique decay behaviors and the impact on vacuum energy, with implications for quantum gravity and cosmology.

Contribution

It explicitly calculates the vacuum expectation values of fermionic condensate and energy-momentum tensor around a cosmic string in de Sitter space, highlighting differences from flat spacetime.

Findings

Fermionic condensate vanishes for massless fields, preserving chiral symmetry.

Vacuum energy-momentum tensor is diagonal with equal axial and radial stresses for massive fields.

String-induced vacuum densities decay as inverse fourth power at large distances, contrasting flat spacetime behavior.

Abstract

We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive spinor field in the geometry of a straight cosmic string on background of de Sitter spacetime. By using the Abel-Plana summation formula, we explicitly extract form the expectation values the contribution associated with purely de Sitter space, remaining the expectation values induced by the cosmic string. The latter presents information about de Sitter gravity as well. Because the investigation of the fermionic quantum fluctuations in de Sitter space have been investigated in literature, here we are mainly interested in the cosmic string-induced contributions. For a massless field, the fermionic condensate vanishes and the presence of the string does not break chiral symmetry of the massless theory. Unlike to the case of a scalar field, for a massive fermionic field the vacuum expectation value of the energy-momentum tensor is diagonal and the axial and radial stresses are equal to the energy density. At large distances from the string the behavior of the string-induced parts in the vacuum densities is damping oscillatory with the amplitude decaying as the inverse fourth power of the distance. This is in contrast to the case of flat spacetime, in which the string-induced vacuum densities for a massive field decay exponentially with distance from the string. In the limit of the large curvature radius of de Sitter space we recover the results for a cosmic string in flat spacetime.