Vacuum polarization by a cosmic string in de Sitter spacetime

TL;DR

This paper studies how a cosmic string influences vacuum polarization effects of a quantum scalar field in higher-dimensional de Sitter space, revealing different asymptotic behaviors depending on the spacetime curvature.

Contribution

It provides a detailed analysis of vacuum polarization induced by a cosmic string in higher-dimensional de Sitter space, including new asymptotic formulas and behavior regimes.

Findings

Vacuum expectation values are finite away from the string.

Different asymptotic behaviors are observed depending on the curvature radius.

Monotonic and oscillatory regimes occur at large distances.

Abstract

In this paper we investigate the vacuum polarization effect associated with a quantum massive scalar field in a higher dimensional de Sitter spacetime in the presence of a cosmic string. Because this investigation has been developed in a pure de Sitter space, here we are mainly interested on the effects induced by the presence of the string. So this analysis is developed by expressing the complete Wightman function as the sum of two terms: The first one corresponds to the bulk where the cosmic string is absent and the second one is induced by the presence of the string. By using the Abel-Plana summation formula, we show that for points away from the string the latter is finite at the coincidence limit and it is used to evaluate the vacuum averages of the square of the field and the energy-momentum tensor induced by the cosmic string. Simple asymptotic formulae are obtained for these expectation values for points near the string and at large distances from it. It is shown that, depending on the curvature radius of de Sitter spacetime, two regimes are realized with monotonic and oscillatory behavior of the vacuum expectation values at large distances.