Fermionic vacuum polarization by a cosmic string in de Sitter spacetime

Abstract

We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive spinor field in de Sitter spacetime in the presence of a straight cosmic string. By using the Abel-Plana summation formula, we explicitly extract from the expectation values the contribution associated with purely de Sitter space, thereafter remaining the expectation values induced by the cosmic string alone. Nevertheless, the latter contains information about de Sitter gravity as well. Because the fermionic quantum vacuum fluctuations in de Sitter space have been investigated in literature, here we are mainly interested in the cosmic string-induced contributions. We observe that for a massless field, the fermionic condensate vanishes and the presence of the string does not break chiral symmetry of the massless theory. Unlike the case of a scalar field, for a massive fermionic field the vacuum expectation value of the energymomentum tensor is diagonal and the axial and radial stresses are equal to the energy density. Moreover, 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 fact 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 large curvature radius of de Sitter space we recover the results for a cosmic string in flat spacetime.