Casimir effect for parallel plates in de Sitter spacetime

Elizalde, E.; Saharian, A. A.; Vardanyan, Tereza

doi:10.1103/physrevd.81.124003

Cited by 37 publications

(23 citation statements)

References 54 publications

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“…This is consistent with Ref. 27, in scalar field case. Notice that the force here is proportional to d −2 , following the square inverse law instead of usually being inverse proportional to fourth power of the separation between two plates, like the expression in (1).…”

Section: Vacuum Fluctuation Force In De Sitter Spacesupporting

confidence: 94%

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Vacuum Fluctuation Force on a Rigid Casimir Cavity in De Sitter and Schwarzschild–de Sitter Space–time

Chen

2012

Int. J. Mod. Phys. A

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We investigate the net force on a rigid Casimir cavity generated by vacuum fluctuations of electromagnetic field in three cases: de Sitter space-time, de Sitter space-time with weak gravitational field and Schwarzschild-de Sitter space-time. In de Sitter space-time the resulting net force follows the square inverse law but unfortunately it is too weak to be measurable due to the large universe radius. By introducing a weak gravitational field into the de Sitter space-time, we find that the net force can now be split into two parts, one is the gravitational force due to the induced effective mass between the two plates and the other one is generated by the metric structure of de Sitter space-time. In order to investigate the vacuum fluctuation force on the rigid cavity under strong gravitational field, we perform a similar analysis in Schwarzschild-de Sitter space-time and results are obtained in three different limits. The most interesting one is when the cavity gets closer to the horizon of a blackhole, square inverse law is recovered and the repulsive force due to negative energy/mass of the cavity now has an observable strength. More importantly the force changes from being repulsive to attractive when the cavity crosses the event horizon, so that the energy/mass of the cavity switches the sign, which suggests the unusual time direction inside the event horizon.

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Section: Vacuum Fluctuation Force In De Sitter Spacesupporting

confidence: 94%

“…While in de Sitter space-time (3 + 1 dimension), the energy-momentum tensor for a conformally coupled massless (ξ = 1/6) scalar field between two plates is given in Ref. 27:…”

Section: Vacuum Fluctuation Force In De Sitter Spacementioning

confidence: 99%

Vacuum Fluctuation Force on a Rigid Casimir Cavity in De Sitter and Schwarzschild–de Sitter Space–time

Chen

2012

Int. J. Mod. Phys. A

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“…Another class of exactly solvable Casimir problems corresponds to de Sitter spacetime. Various geometries of boundaries in this background have been considered [40][41][42][43][44][45][46][47][48][49]. In inflationary coordinates the corresponding metric is time-dependent and, in general, in addition to the diagonal component, the vacuum energy-momentum tensor has a nonzero off-diagonal component that describes an energy flux along the direction normal to the boundary.…”

Section: Introductionmentioning

confidence: 99%

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

2014

Self Cite

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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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“…We should also bring to the attention of the general reader the important work on the Casimir effect in [33,34], where the authors have studied a massive scalar field with arbitrary curvature-coupling parameter, in the region between two infinite parallel plates, on a de The explicit expression of the Christoffel symbols in closed-slicing coordinate system reads as follows. As above, by expanding in powers of ε such connection coefficients, that is,…”

Section: Discussionmentioning

confidence: 99%

Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime

Esposito

Napolitano

2015

Phys. Scr.

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Recent work in the literature has studied rigid Casimir cavities in a weak gravitational field, or in de Sitter spacetime, or yet other spacetime models. The present review paper studies the difficult problem of direct evaluation of scalar Green functions for a Casimir-type apparatus in de Sitter spacetime. Working to first order in the small parameter of the problem, i.e. twice the gravity acceleration times the plates' separation divided by the speed of light in vacuum, suitable coordinates are considered for which the differential equations obeyed by the zeroth-and firstorder Green functions can be solved in terms of special functions. This result can be used, in turn, to obtain, via the point-split method, the regularized and renormalized energy-momentum tensor both in the scalar case and in the physically more relevant electromagnetic case.

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Casimir effect for parallel plates in de Sitter spacetime

Cited by 37 publications

References 54 publications

Vacuum Fluctuation Force on a Rigid Casimir Cavity in De Sitter and Schwarzschild–de Sitter Space–time

Vacuum Fluctuation Force on a Rigid Casimir Cavity in De Sitter and Schwarzschild–de Sitter Space–time

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

Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime

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