Effects of Curvature-Scalar Coupling on Vacuum Energy in Flat (3+1)-Dimensional Space-Time

Abstract

We investigated how a magnetic topological defect affects the vacuum polarization of a charged massive scalar field in a flat $(3+1)$-dimensional space-time. The defect was modeled as an impenetrable to matter field finite-thickness tube with magnetic flux inside. We implemented the most general form of the Robin boundary condition on the surface of the magnetic tube, which enables a fully general analysis of the problem. We have found that in flat spacetime, the total vacuum energy generated by a magnetic topological defect depends on the curvature $\xi$, except for special cases corresponding to the Dirichlet and Neumann boundary conditions. By contrast, when Robin's general boundary conditions are imposed, the induced vacuum energy acquires an explicit dependence on the curvature coupling $\xi$, which is significant even in flat space-time. A detailed study of the dependence of the effect on the boundary condition parameter has been carried out. The obtained results highlight the nontrivial role played by boundary conditions in vacuum polarization phenomena.

arXiv comment12 pages, 3 figures

References in corpus (17)

• New Developments in the Casimir Effect
• Heat kernel expansion: user's manual
• Sakharov's induced gravity: a modern perspective
• The ground state energy of a spinor field in the background of a finite radius flux tube
• Multiple reflection expansion and heat kernel coefficients
• The Casimir-Aharonov-Bohm effect?
• Non-Minimal Coupling of the Higgs Boson to Curvature in an Inflationary Universe
• Direct Higgs-gravity interaction and stability of our Universe
• Polarization of the vacuum of a quantized scalar field by an impenetrable magnetic vortex of finite thickness
• Induced vacuum energy-momentum tensor in the background of a d-2 - brane in d+1 - dimensional space-time
• Vacuum energy induced by an impenetrable flux tube of finite radius
• Casimir energy and force induced by an impenetrable flux tube of finite radius
• The non-minimal coupling constant and the primordial de Sitter state
• Magnetic flux in the vacuum of quantum bosonic matter in the cosmic string background
• Testing Gravity and Predictions Beyond the Standard Model at Short Distances: The Casimir Effect
• Induced vacuum energy density of quantum charged scalar matter in the background of an impenetrable magnetic tube with the Neumann boundary condition
• Dependence of scalar matter vacuum energy, induced by a magnetic topological defect, on the coupling to space-time curvature