Scalar Casimir Effect on a D-dimensional Einstein Static Universe

Abstract

We compute the renormalised energy momentum tensor of a free scalar field coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU), RxS^n, with arbitrary low energy effective operators (up to mass dimension n+1). A generic class of regulators is used, together with the Abel-Plana formula, leading to a manifestly regulator independent result. The general structure of the divergences is analysed to show that all the gravitational couplings (not just the cosmological constant) are renormalised for an arbitrary regulator. Various commonly used methods (damping function, point-splitting, momentum cut-off and zeta function) are shown to, effectively, belong to the given class. The final results depend strongly on the parity of n. A detailed analytical and numerical analysis is performed for the behaviours of the renormalised energy density and a quantity `sigma' which determines if the strong energy condition holds for the `quantum fluid'. We briefly discuss the quantum fluid back-reaction problem, via the higher dimensional Friedmann and Raychaudhuri equations, observe that equilibrium radii exist and unveil the possibility of a `Casimir stabilisation of Einstein Static Universes'.

37 pages, 15 figures, v2: minor changes in sections 1, 2.5, 3 and 4; version published in CQG

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Cited by in corpus (13)

• The Casimir Force in Randall Sundrum Models with q+1 dimensions
• Casimir effect within D=3+1 Maxwell-Chern-Simons electrodynamics
• Casimir Effect in Spacetime with Extra Dimensions -- From Kaluza-Klein to Randall-Sundrum Models
• DeWitt-Schwinger Renormalization and Vacuum Polarization in d Dimensions
• Radiative Correction to the Casimir Energy for Massive Scalar Field on a Spherical Surface
• Double-well instantons in finite volume
• Casimir effect in hemisphere capped tubes
• Casimir energy calculation for massive scalar field on spherical surfaces: an alternative approach
• Thermal Casimir effect in the Einstein Universe with a spherical boundary
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• Cosmology with quantum matter and a classical gravitational field: the approach of configuration-space ensembles
• The Casimir spectrum revisited
• Equivalence of zeta function technique and Abel-Plana formula in regularizing the Casimir energy of hyper-rectangular cavities