Vacuum polarization by a cosmic string in de Sitter spacetime

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.

18 pages, 2 figures, discussion on string metric in static coordinates is added

References in corpus (7)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• Casimir effect in de Sitter spacetime with compactified dimension
• Wightman function and vacuum densities in de Sitter spacetime with toroidally compactified dimensions
• Fermionic vacuum polarization by a composite topological defect in higher-dimensional space-time
• Cosmic strings in a space-time with positive cosmological constant