Stress-energy tensor for a quantized bulk scalar field in the Randall-Sundrum brane model

Knapman, Alan; Toms, David J.

doi:10.1103/physrevd.69.044023

Cited by 65 publications

(85 citation statements)

References 27 publications

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“…The evaluation of these characteristics requires the knowledge of a complete set of modes for a quantum field and exact results can be provided for highly symmetric bulk and boundary geometries only. In particular, motivated by the problems of the radion stabilization and the cosmological constant generation in braneworld models, the Casimir effect for planar boundaries in antide Sitter space has been widely discussed [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Higherdimensional generalizations of the anti-de Sitter background having compact internal spaces have been considered as well [32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Wightman function and the Casimir effect for a Robin sphere in a constant curvature space

2014

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We evaluate the Wightman function, the mean field squared and the vacuum expectation value of the energy-momentum tensor for a scalar field with the Robin boundary condition on a spherical shell in the background of a constant negative curvature space. For the coefficient in the boundary condition there is a critical value above which the scalar vacuum becomes unstable. In both the interior and the exterior regions, the vacuum expectation values are decomposed into the boundary-free and sphere-induced contributions. For the latter, rapidly convergent integral representations are provided. In the region inside the sphere, the eigenvalues are expressed in terms of the zeros of the combination of the associated Legendre function and its derivative and the decomposition is achieved by making use of the Abel-Plana type summation formula for the series over these zeros. The sphere-induced contribution to the vacuum expectation value of the field squared is negative for the Dirichlet boundary condition and positive for the Neumann one. At distances from the sphere larger than the curvature scale of the background space the suppression of the vacuum fluctuations in the gravitational field corresponding to the negative curvature space is stronger compared with the case of the Minkowskian bulk. In particular, the decay of the vacuum expectation values with the distance is exponential for both massive and massless fields. The corresponding results are generalized for spaces with spherical bubbles and for cosmological models with negative curvature spaces.

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Section: Introductionmentioning

confidence: 99%

Wightman function and the Casimir effect for a Robin sphere in a constant curvature space

2014

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“…Local Casimir densities were considered in Refs. [3,4]. The Casimir effect in higher-dimensional generalizations of the AdS spacetime with compact internal spaces has been investigated in [5].…”

Section: Introductionmentioning

confidence: 99%

Casimir effect for parallel plates in de Sitter spacetime

2010

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The Wightman function and the vacuum expectation values of the field squared and of the energy-momentum tensor are obtained, for a massive scalar field with an arbitrary curvature coupling parameter, in the region between two infinite parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. For the calculation, a mode-summation method is used, supplemented with a variant of the generalized Abel-Plana formula. This allows to explicitly extract the contributions to the expectation values which come from each single boundary, and to expand the second-plate-induced part in terms of exponentially convergent integrals. Several limiting cases of interest are then studied. Moreover, the Casimir forces acting on the plates are evaluated, and it is shown that the curvature of the background spacetime decisively influences the behavior of these forces at separations larger than the curvature scale of de Sitter spacetime. In terms of the curvature coupling parameter and the mass of the field, two very different regimes are realized, which exhibit monotonic and oscillatory behavior of the vacuum expectation values, respectively. The decay of the Casimir force at large plate separation is shown to be power-law (monotonic or oscillating), with independence of the value of the field mass.

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“…The energy-momentum tensor in the Randall-Sundrum braneworld for a bulk scalar with zero brane mass terms c 1 and c 2 is considered in Ref. 18. In this paper only a general formula is given for the unrenormalized VEV in terms of the differential operator acting on the Green function.…”

Section: Quantum Effects In Higher-dimensional Cosmological Models 171mentioning

confidence: 99%

“…Due to the maximal symmetry of AdS spacetime one has T k i AdS = const·g ik . The boundary-induced part is given by the expressions (18) where…”

Section: Casimir Densities For a Single Branementioning

confidence: 99%

Quantum Effects in Higher-Dimensional Cosmological Models

Saharian

2012

Int. J. Mod. Phys. Conf. Ser.

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Vacuum energy density and stresses are investigated for a scalar field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions and in antide Sitter spacetime with two parallel branes. On the branes the field obeys the Robin boundary conditions. The behavior of the vacuum expectation values is discussed in various asymptotic regions of the parameters. Applications are given to Randall-Sundrum type braneworlds.

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Stress-energy tensor for a quantized bulk scalar field in the Randall-Sundrum brane model

Cited by 65 publications

References 27 publications

Wightman function and the Casimir effect for a Robin sphere in a constant curvature space

Wightman function and the Casimir effect for a Robin sphere in a constant curvature space

Casimir effect for parallel plates in de Sitter spacetime

Quantum Effects in Higher-Dimensional Cosmological Models

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