Vacuum Polarization Induced by a Boundary in de Sitter Space with Compact Dimensions

Saharian, A. A.; Simonyan, D. H.; Kotanjyan, A. S.

doi:10.3103/s1068337219010018

Cited by 3 publications

(1 citation statement)

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“…The VEVs in geometries with spherical dS bubbles have been investigated in [28]. The topological Casimir effect induced by toroidal compactification of a part of spatial dimensions and by the presence of topological defects in locally dS spacetime was discussed in [29]- [37].…”

Section: Introductionmentioning

confidence: 99%

Casimir densities induced by a sphere in the hyperbolic vacuum of de Sitter spacetime

Saharian,

Petrosyan

2021

Preprint

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Complete set of modes and the Hadamard function are constructed for a scalar field inside and outside a sphere in (D + 1)-dimensional de Sitter spacetime foliated by negative constant curvature spaces. We assume that the field obeys Robin boundary condition on the sphere. The contributions in the Hadamard function induced by the sphere are explicitly separated and the vacuum expectation values (VEVs) of the field squared and energy-momentum tensor are investigated for the hyperbolic vacuum. In the flat spacetime limit the latter is reduced to the conformal vacuum in the Milne universe and is different from the maximally symmetric Bunch-Davies vacuum state. The vacuum energy-momentum tensor has a nonzero off-diagonal component that describes the energy flux in the radial direction. The latter is a purely sphere-induced effect and is absent in the boundary-free geometry. Depending on the constant in Robin boundary condition and also on the radial coordinate, the energy flux can be directed either from the sphere or towards the sphere. At early stages of the cosmological expansion the effects of the spacetime curvature on the sphere-induced VEVs are weak and the leading terms in the corresponding expansions coincide with those for a sphere in the Milne universe. The influence of the gravitational field is essential at late stages of the expansion. Depending on the field mass and the curvature coupling parameter, the decay of the sphere-induced VEVs, as functions of the time coordinate, is monotonic or damping oscillatory. At large distances from the sphere the fall-off of the sphere-induced VEVs, as functions of the geodesic distance, is exponential for both massless and massive fields.

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Section: Introductionmentioning

confidence: 99%