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

Abstract

For the electromagnetic field in [Formula: see text]-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 [Formula: see text] because of the conformal invariance of the electromagnetic field and is directed towards the cosmic string for [Formula: see text]. The topological contributions in the vacuum stresses are anisotropic and, unlike the geometry of a cosmic string in the Minkowski spacetime, for [Formula: see text] 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 and the leading terms in the respective expansions coincide with the expectation values for a cosmic string in the background of Minkowski spacetime. 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 [Formula: see text]. The exception is the energy density in the special case [Formula: see text]. For a cosmic string in the Minkowski bulk the energy flux is absent and the diagonal components are proportional to the [Formula: see text]th power of the inverse distance.