The Casimir Densities for a Sphere in the Milne Universe

Saharian, A. A.; Petrosyan, T. A.

doi:10.3390/sym12040619

Cited by 9 publications

(15 citation statements)

References 69 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The flat spacetime counterpart of the H-vacuum is the conformal vacuum in the Milne universe (for the investigation of the corresponding VEVs induced by a spherical boundary see [42]). The flat spacetime limit for the BD vacuum corresponds to the Minkowski vacuum.…”

Section: Discussionmentioning

confidence: 99%

Mean field squared and energy-momentum tensor for the hyperbolic vacuum in dS spacetime

Saharian,

Petrosyan,

Torosyan

2021

Preprint

View full text Add to dashboard Cite

We evaluate the Hadamard function and the vacuum expectation values (VEVs) of the field squared and energy-momentum tensor for a massless conformally coupled scalar field in (D + 1)-dimensional de Sitter (dS) spacetime foliated by spatial sections of negative constant curvature. It is assumed that the field is prepared in the hyperbolic vacuum state. An integral representation for the difference of the Hadamard functions corresponding to the hyperbolic and Bunch-Davies vacua is provided that is well adapted for the evaluation of the expectation values in the coincidence limit. It is shown that the Bunch-Davies state is interpreted as thermal with respect to the hyperbolic vacuum. An expression for the corresponding density of states is provided. The relations obtained for the difference in the VEVs for the Bunch-Davies and hyperbolic vacua are compared with the corresponding relations for the Fulling-Rindler and Minkowski vacua in flat spacetime. The similarity between those relations is explained by the conformal connection of dS spacetime with hyperbolic foliation and Rindler spacetime. As a limiting case, the VEVs for the conformal vacuum in the Milne universe are discussed.

show abstract

Section: Discussionmentioning

confidence: 99%

Mean field squared and energy-momentum tensor for the hyperbolic vacuum in dS spacetime

Saharian,

Petrosyan,

Torosyan

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The expression of the Wightman function for the conformal vacuum (denoted here as C ( , ) W x x′ ) can be obtained by using the corresponding formula for the Hadamard function from [13]:…”

Section: Wightman Functions In Conformal and Minkowski Vacuamentioning

confidence: 99%

“…The corresponding geometry serves as a simple model for the investigation of quantum-field-theoretical effects in time-dependent backgrounds. A relatively large number of problems are exactly solvable and motivated by that various aspects of the dynamics of quantum fields in the Milne universe have been discussed in [4][5][6][7][8][9][10][11][12][13]. In the present paper we consider the local characteristics of the conformal vacuum state (referred to as the C-vacuum) for a massless scalar field in the Milne universe.…”

Section: Introductionmentioning

confidence: 99%

Polarization of the Conformal Vacuum in the Milne Universe

Petrosyan

2021

Armenian Journal of Physics

View full text Add to dashboard Cite

The vacuum expectation values of the field squared and energy-momentum tensor for a massless scalar field are investigated in the Milne universe with general number of spatial dimensions. The vacuum state depends on the choice of the mode functions in the canonical quantization procedure and we assume that the field is prepared in the conformal vacuum. As the first step an integral representation for the difference of the Wightman functions corresponding to the conformal and Minkowski vacua is derived. The mean field squared and energy-momentum tensor are obtained in the coincidence limit. It is shown that the Minkowski vacuum state is interpreted as a thermal one with respect to the conformal vacuum. The thermal factor is of the Bose-Einstein type in odd dimensional space and of the Fermi-Dirac type in even number of spatial dimensions.

show abstract

“…It can be checked that this formula is obtained from the corresponding expression in [48] by making use of the addition theorem (B.2).…”

Section: Boundary-free Geometrymentioning

confidence: 99%

“…from (4.29) the boundary-induced Hadamard function is obtained outside the sphere in the Milne universe [48].…”

Section: 18)mentioning

confidence: 99%

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

Saharian,

Petrosyan

2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

The Casimir Densities for a Sphere in the Milne Universe

Cited by 9 publications

References 69 publications

Mean field squared and energy-momentum tensor for the hyperbolic vacuum in dS spacetime

Mean field squared and energy-momentum tensor for the hyperbolic vacuum in dS spacetime

Polarization of the Conformal Vacuum in the Milne Universe

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

Contact Info

Product

Resources

About