Electromagnetic vacuum stresses and energy fluxes induced by a cosmic string in de Sitter spacetime

TL;DR

This paper investigates how a cosmic string in de Sitter spacetime influences electromagnetic vacuum stresses and energy fluxes, revealing anisotropic effects and decay behaviors depending on the spacetime dimension and distance from the string.

Contribution

It provides explicit calculations of the vacuum energy-momentum tensor's topological contributions in higher-dimensional de Sitter space with a cosmic string, including off-diagonal energy flux components.

Findings

Energy flux is directed towards the string for D≥4.

Topological stresses are anisotropic and depend on the distance from the string.

At large distances, vacuum contributions decay as inverse powers of the distance.

Abstract

For the electromagnetic field in (D+1)-dimensional locally de Sitter (dS) spacetime, we analyze the effects of a generalized cosmic string type defect on the vacuum expectation value of the energy-momentum tensor. For the Bunch-Davies vacuum state, the topological contributions are explicitly extracted in both the diagonal and off-diagonal components. The latter describes the presence of radially directed energy flux in the vacuum state. It vanishes for $D=3$ because of the conformal invariance of the electromagnetic field and is directed towards the cosmic string for $D\geq 4$ . The topological contributions in the vacuum stresses are anisotropic and, unlike to the geometry of a cosmic string in the Minkowski spacetime, for $D>3$ the stresses along the directions parallel to the string core differ from the energy density. Depending on the planar angle deficit and the distance from the cosmic string, the corresponding expectation values can be either positive or negative. Near the cosmic string the effect of the gravitational field on the diagonal components of the topological part is weak. The spacetime curvature essentially modifies the behavior of the topological terms at proper distances from the cosmic string larger than the dS curvature radius. In that region, the topological contributions in the diagonal components of the energy-momentum tensor decay in inverse proportion to the fourth power of the proper distance and the energy flux density behaves as inverse-fifth power for all values of the spatial dimension $D$. The exception is the energy density in the special case $D=4$.