The Casimir densities are investigated for a massive spinor field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The vacuum expectation value of the energy-momentum tensor is presented in the form of the sum of corresponding quantity in the uncompactified de Sitter spacetime and the part induced by the non-trivial topology. The latter is finite and the renormalization is needed for the first part only. The asymptotic behavior of the topological term is investigated in the early and late stages of the cosmological expansion. When the comoving lengths of the compactified dimensions are much smaller than the de Sitter curvature radius, to the leading order the topological part coincides with the corresponding quantity for a massless fermionic field and is conformally related to the corresponding flat spacetime result with the same topology. In this limit the topological term dominates the uncompactified de Sitter part and the back-reaction effects should be taken into account. In the opposite limit, for a massive field the asymptotic behavior of the topological part is damping oscillatory.
Casimir effect for massless minimally coupled scalar field is studied. An explicit answer for de Sitter spacetime is obtained and analized. Cosmological implications of the result are discussed.
We investigate the Hadamard function, the vacuum expectation values of the field square and the energy-momentum tensor of a scalar field with general curvature coupling parameter in de Sitter spacetime compactified along one of spatial dimensions. By using the Abel-Plana summation formula, we have explicitly extracted from the vacuum expectation values the part due to the compactness of the spatial dimension. The topological part in the vacuum energy-momentum tensor violates the local de Sitter symmetry and dominates in the early stages of the cosmological evolution. At late times the correspo…
We demonstrate that the static ground state atom, which interacts with a conformally coupled massless scalar field in the de Sitter invariant vacuum, can obtain a position-dependent energy-level shift and this shift could cause a Casimir-Polder-like force on it. Interestingly no such force arises on the inertial atom bathed in a thermal radiation in the Minkowski universe. Thus, although the energy-level shifts of the static atom for these two cases are structurally the same, whether the energy-level shift causes the Casimir-Polder-like force, in principle, could be as an indicator to distingu…
In this paper, we evaluate the Casimir energy and pressure for a massive fermionic field confined in the region between two parallel plates. In order to implement this confinement we impose the standard MIT bag boundary on the plates for the fermionic field. In this paper we consider a quantum field theory model with a CPT even, aether-like Lorentz symmetry violation. It turns out that the fermionic Casimir energy and pressure depend on the direction of the constant vector that implements the Lorentz symmetry breaking.
The vacuum energy for a massless conformally coupled scalar field in a brane world set up, corresponding to de Sitter branes in a bulk anti-de Sitter spacetime, is calculated. We use the Euclidean version of the metric which can be conformally related to a metric similar in form to the Einstein universe (S^4 times R). Employing zeta-function regularisation we evaluate the one-loop effective potential and show that the vacuum energy is zero for the one brane and non-zero for the two brane configuration. We comment on the back-reaction of this Casimir energy and on the inclusion of a mass term o…
We compute the Casimir energy of the photon field in a de Sitter space and find it to be proportional to the size of the horizon, the same form of the holographic dark energy. We suggest to make metamaterials to mimic de Sitter space in laboratory and measure the predicted Casimir energy.
Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods, the Schwarzschild-de Sitter and the de Sitter space energy difference. By computing the one loop approximation for TT tensors we discover the existence of an unstable mode even for the non-degenerate case. This result seems to be in agreement with the sub-maximal black hole pair creation of Bousso-Hawking. The instability can be eliminated by the boundary reduction method. Implications on a foam-like space are discussed.
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 first-order Green functi…
We study the finite temperature Casimir interactions on two parallel boundaries in the anti-de Sitter spacetime AdS$_{D+1}$ induced by the vacuum fluctuations of a massive fermionic field with MIT bag boundary conditions. As in the Minkowski spacetime, the Casimir interaction always tends to attract the two boundaries to each other at any temperature and for any mass. For bosonic fields, it is well known that the high temperature leading term of the Casimir interaction is linear in temperature. However, for fermionic fields, the Casimir interaction decays exponentially at high temperature due …
Based on some recent work of the authors, we focus on the relationship between the Casimir energy of a Majorana spinor field for a Euclidean Einstein universe $S^4\times R$ and for a Euclidean de Sitter brane ($S^4$) embedded in AdS(5). This is for a conformally coupled massless field. Interestingly, the one brane effective potential is zero and the results are equivalent, as for the scalar case, when evaluated on the conformally related cylinder. However, using the actual metric this equivalence no longer holds because a non-trivial contribution from the path integral measure (known as the co…
The Casimir stress on two concentric spherical shell in de Sitter background for massless scalar field is calculated. The scalar field satisfies Dirichlet boundary conditions on the spheres. The metric is written in conformally flat form to make maximum use of Minkowski space calculations. Then the Casimir stress is calculated for inside and outside of the shell with different backgrounds. This model may be used to study the effect of the Casimir stress on the dynamics of the domain wall formation in inflationary models of early universe.
We investigate the fermionic condensate and the vacuum expectation values of the energy-momentum tensor for a massive spinor field in de Sitter spacetime with spatial topology $\mathrm{R}^{p}\times (\mathrm{S}^{1})^{q}$. Both cases of periodicity and antiperiodicity conditions along the compactified dimensions are considered. By using the Abel-Plana formula, the topological parts are explicitly extracted from the vacuum expectation values. In this way the renormalization is reduced to the renormalization procedure in uncompactified de Sitter spacetime. It is shown that in the uncompactified su…
The Casimir stress on a spherical shell in de Sitter signature changing background for massless scalar field satisfying Dirichlet boundary conditions on the shell is calculated. The Casimir stress is calculated for inside and outside of the shell with different backgrounds corresponding to different metric signatures and cosmological constants. An important contribution appears due to signature change which leads to a transient rapid expansion of the bubbles in this background.
The influence of an external constant uniform magnetic field on the Casimir energy density of a Dirac field under antiperiodic (and periodic) boundary condition is computed by applying Schwinger's proper time method. The result thus obtained shows that in principle, under suitable conditions, the magnetic field can enhance the fermionic Casimir energy density.
The Casimir stress on cylinderical shell in de Sitter background for massless scalar field satisfying Dirichlet boundary conditions on the cylinder is calculated. The metric is written in conformally flat form to make maximum use of the Minkowski space calculations. Different cosmological constants are assumed for the space inside and outside the cylinder to have general results applicable to the case of cylindrical domain wall formations in the early universe.
The Casimir stress on two parallel plates in de Sitter background for massless scalar field satisfying Robin boundary conditions on the plates is calculated. The metric is written in conformally flat form to make maximum use of the Minkowski space calculations. Different cosmological constants are assumed for the space between and outside of the plates to have general results applicable to the case of domain wall formations in the early universe.
The energy-momentum tensor for a massless conformally coupled scalar field in de Sitter spacetime in the presence of a couple curved branes is investigated. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.
We discuss the bulk Casimir effect (effective potential) for a conformal or massive scalar when the bulk represents five-dimensional AdS or dS space with two or one four-dimensional dS brane, which may correspond to our universe. Using zeta-regularization, the interesting conclusion is reached, that for both bulks in the one-brane limit the effective potential corresponding to the massive or to the conformal scalar is zero. The radion potential in the presence of quantum corrections is found. It is demonstrated that both the dS and the AdS braneworlds may be stabilized by using the Casimir for…
The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two 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. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime d…
Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for twisted and untwisted massive spinor fields in higher-dimensional de Sitter spacetime with toroidally compactified spatial dimensions. The expectation values are presented in the form of the sum of corresponding quantities in the uncompactified de Sitter spacetime and the parts induced by non-trivial topology. The latter are finite and the renormalization is needed for the first parts only. Closed formulae are derived for the renormalized fermionic vacuum densities in uncompactified odd-di…
We investigate the vacuum expectation value of the energy-momentum tensor associated with a massive fermionic field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. The asymptotic behavior of the vacuum densities is investigated near the sphere center and surface, and at large distances from the sphere. In the limit of strong gravitational field corresponding to small values of the parameter describing the solid angle deficit in global monopole geometry, the sphere-induced expectation values are exponentially suppressed.
The aim of this work is to investigate the role played by the fermion mass and that of an external field on the fermionic Casimir energy density under S^1 X R^3 topology. Both twisted and untwisted spin connections are considered and the exact calculation is performed using a somewhat different approach based on the combination of the analytic regularization method through alpha-representation and Euler-Maclaurin summation formula.
In this paper, we analyze the fermionic Casimir effects associated with a massless quantum field in the context of Lorentz symmetry violation approach based on Horava-Lifshitz methodology. In order to obtain these observables, we impose the standard MIT bag boundary condition on the fields on two large and parallel plates. Our main objectives are to investigate how the Casimir energy and pressure depend on the parameter associated with the breaking of Lorentz symmetry.
We calculate the one-loop effective action of a scalar field with general mass and coupling to the curvature in the detuned Randall-Sundrum brane world scenario, where the four-dimensional branes are anti-de Sitter. We make use of conformal transformations to map the problem to one on the direct product of the hyperbolic space H^4 and the interval. We also include the cocycle function for this transformation. This Casimir potential is shown to give a sizable correction to the classical radion potential for small values of brane separation.
Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods, the Schwarzschild-Anti-de Sitter and the Anti-de Sitter space energy difference. By computing the one loop approximation for TT tensors we discover the existence of an unstable mode at zero temperature, which can be stabilized by the boundary reduction method. Implications on a foam-like space are discussed.
We consider the finite temperature Casimir effect of a massive fermionic field confined between two parallel plates, with MIT bag boundary conditions on the plates. The background spacetime is $M^{p+1}\times T^q$ which has $q$ dimensions compactified to a torus. On the compact dimensions, the field is assumed to satisfy periodicity boundary conditions with arbitrary phases. Both the high temperature and the low temperature expansions of the Casimir free energy and the force are derived explicitly. It is found that the Casimir force acting on the plates is always attractive at any temperature r…
The Casimir stress on a cylinderical shell in background of conformally flat space-time for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.
Starting from the well-known quantum Miura-like transformation for the non simply-laced Lie algebras B(3),we give an explicit construction of the Casimir WB(3) algebras.We reserve the notation WB(N) for the Casimir W algebras of type W(2,4,6,...,2N,N+1/2) which contains one fermionic field. It is seen that WB(3) algebra is closed an associative for all values of the central element c.
We evaluate the Casimir energy and force for a massive fermionic field in the geometry of two parallel plates on background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions. The bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The Casimir energy is decomposed into purely topological, single plate and interaction parts. With independence of the lengths of the compact dimensions and the phases in the periodicity conditions, the interaction part of the Casimi…
We consider a quantum massless fermionic field in (1+1) dimensions in the case of moving boundaries. We work in the canonical approach in order to find a Hamiltonian describing the dynamics of the field. Thus, we study the statistics of work and particles produced from the vacuum by a linear driving of a boundary.
We use a functional approach to calculate the Casimir energy due to Dirac fields in interaction with thin, flat, parallel walls, which implement imperfect bag-like boundary conditions. These are simulated by the introduction of delta-like interactions with the walls. We show that, with a proper choice for the corresponding coupling constants, bag-model boundary condition are properly implemented. We obtain explicit expressions for the energies in 1+1 and 3+1 dimensions, for massless and massive fields.
Vacuum expectation values of the energy-momentum tensor for a conformally coupled scalar field is investigated in de Sitter (dS) spacetime in presence of a curved brane on which the field obeys the Robin boundary condition with coordinate dependent coefficients. To generate the corresponding vacuum densities we use the conformal relation between dS and Rindler spacetimes and the results previously obtained by one of the authors for the Rindler counterpart. The resulting energy-momentum tensor is non-diagonal and induces anisotropic vacuum stresses. The asymptotic behaviour of this tensor is in…
We study two fermionic systems that have an underlying supersymmetric structure, namely a color superconductor and Dirac fermion in a Reissner-Nordström-anti-de Sitter gravitational background. In the chiral limit of the color superconductor, the localized fermionic zero modes around the vortex form an N=2 with zero central charge $d=1$ quantum algebra, with all the operators being Fredholm. We compute the Witten index of this algebra and we find an unbroken supersymmetry. The fermionic gravitational system in the chiral limit too, has two underlying unbroken N=2, $d=1$ supersymmetric algebras…
In eikonal and quenched approximation, it is argued that the strong coupling fermionic QCD Green's functions and related amplitudes depart from a sole dependence on the SUc(3) quadratic Casimir operator, C2f, evaluated over the fundamental gauge group representation. Noticed in non-relativistic Quark Models and in a non-perturbative generalization of the Schwinger mechanism, an additional dependence on the cubic Casimir operator shows up, in contradistinction with perturbation theory and other non-perturbative approaches. However, it accounts for the full algebraic content of the rank-2 Lie al…
Vacuum energy density and stresses are investigated for a scalar field with general curvature coupling parameter in (D+1)-dimensional de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The corresponding expectation values are presented in the form of the sum of the vacuum expectation values in uncompactified dS spacetime and the part induced by the non-trivial topology. In the early stages of the cosmological evolution the topological parts dominate. In this limit the behavior of the Casimir densities does not depend on the curvature coupling parameter …
We investigate the net force on a rigid Casimir cavity generated by vacuum fluctuations of electromagnetic field in three cases, de Sitter spacetime, de Sitter spacetime with weak gravitational field and Schwarzschild-de Sitter spacetime. In de Sitter spacetime 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 spacetime, we find the net force now can be splited into two parts, one is the gravitational force due to the induced effective mass betwe…
In this work, we consider the Casimir effect due to massless fermionic fields in the presence of long cylinders. More precisely, we consider the interaction between a cylinder parallel to a plate, between two parallel cylinders outside each other, and between a cylinder lying parallelly inside another cylinder. We derive the explicit formulas for the Casimir interaction energies and compute the leading and the next-to-leading order terms of the small separation asymptotic expansions. As expected, the leading order terms coincide with the proximity force approximations. We compare the results o…
In this paper, we consider the fermionic Casimir effect under a new type of space-time topology using the concept of quotient topology. The relation between the new topology and that in Ref. \cite{Feng,Zhai3} is something like that between a Möbius strip and a cylindric. We obtain the exact results of the Casimir energy and force for the massless and massive Dirac fields in the ($D+1$)-dimensional space-time. For both massless and massive cases, there is a $Z_2$ symmetry for the Casimir energy. To see the effect of the mass, we compare the result with that of the massless one and we found that…
Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for a massive spinor fields in higher-dimensional spacetimes with an arbitrary number of toroidally compactified spatial dimensions. By using the Abel-Plana summation formula and the zeta function technique we present the vacuum expectation values in two different forms. Applications of the general formulae to cylindrical and toroidal carbon nanotubes are given. We show that the topological Casimir energy is positive for metallic cylindrical nanotubes and is negative for semiconducting ones. T…
Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor are investigated for a scalar field with general curvature coupling parameter in the geometry of a plate in the de Sitter spacetime. Robin boundary condition for the field operator is assumed on the plate. The vacuum expectation values are presented as the sum of two terms. The first one corresponds to the geometry of de Sitter bulk without boundaries and the second one is induced by the presence of the plate. We show that for non-conformal fields the vacuum energy-momentum tensor is non-diagon…
In this article we consider the Casimir energy and force of massless Majorana fermions and vector bosons between parallel plates. The vector bosons satisfy perfect electric conductor boundary conditions while the Majorana fermions satisfy bag and chiral boundary conditions. We consider various piston configurations containing one vector boson and one fermion. We present a new regularization mechanism the piston offers. In our case regularization occurs explicitly at the Casimir energy density and not at the Casimir force level, as in usual pistons. We make use of boundary broken supersymmetry …
We evaluate the fermionic Casimir effect associated with a massive fermion confined within a planar (d+1) dimensional slab-bag, on which MIT bag model boundary conditions of standard type, along a single spatial direction, are imposed. A simple and effective method for adding up the zero-point energy eigenvalues, corresponding to a quantum field under the influence of arbitrary boundary conditions, imposed on the field on flat surfaces perpendicular to a chosen spatial direction, is proposed. Using this procedure, an analytic result is obtained, from which small and large fermion mass limits, …
In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS$_{4+1}$ spacetime. We will consider the general plane--symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentu…
The fermionic condensate and vacuum expectation value of the energy-momentum tensor, for a massive fermionic field on the background of anti-de Sitter spacetime, in the geometry of two parallel boundaries with bag boundary conditions, are investigated. Vacuum expectation values, expressed as series involving the eigenvalues of the radial quantum number, are neatly decomposed into boundary-free, single-boundary-induced, and second-boundary-induced parts, with the help of the generalized Abel-Plana summation formula. In this way, the renormalization procedure is very conveniently reduced to the …
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 …
We investigate two measures of quantum correlations and entanglement, namely the violation of the Bell-Mermin-Klyshko inequalities and the quantum discord, for Dirac fermions in the cosmological de Sitter background of dimension four. The BMK violation is focussed on the vacuum for two and four mode squeezed states and it is shown to increase with the number of modes. For the quantum discord, we investigate a maximally entangled in-vacuum state. Qualitative similarities as well as differences of our results with that of different coordinatisations of de Sitter in the context of scalar and ferm…
We investigate combined effects of nontrivial topology, induced by a cosmic string, and boundaries on the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field. As geometry of boundaries we consider two plates perpendicular to the string axis on which the field is constrained by the MIT bag boundary condition. By using the Abel-Plana type summation formula, the VEVs in the region between the plates are decomposed into the boundary-free and boundary-induced contributions for general case of the planar angle deficit. The boundary-…
Fermionic condensate is investigated in $(D+1)$-dimensional de Sitter spacetime by using the cutoff function regularization. In order to fix the renormalization ambiguity for massive fields an additional condition is imposed, requiring the condensate to vanish in the infinite mass limit. For large values of the field mass the condensate decays exponentially in odd dimensional spacetimes and follows a power law decay in even dimensional spacetimes. For a massless field the fermionic condensate vanishes for odd values of the spatial dimension $D$ and is nonzero for even $D$. Depending on the spa…
We estimate the dominating frequencies contributing to the Casimir energy in a cavity of metamaterials mimicking de Sitter space, by solving the eigenvalue problem of Maxwell equations. It turns out the dominating frequencies are the inverse of the size of the cavity, and the degeneracy of these frequencies also explains our previous result on the unusually large Casimir energy. Our result suggests that carrying out the experiment in laboratory is possible theoretically.
We consider the Casimir interaction, mediated by massless fermions, between a spherical defect and a flat potential barrier, assuming hard (bag-type) boundary conditions at both the barrier and the surface of the sphere. The computation of the quantum interaction energy is carried out using the multiple scattering approach, adapted here to the setup in question. We find an exact integral formula for the energy, from which we extract both the large and short distance asymptotic behaviour. At large distance the fermionic contribution is found to scale as $L^{-3}$, in contrast to that of electrom…
The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the Möbius domain-wall fermion formulation, in the $1+1$-, $2+1$-, and $3+1$-dimensional space-time with the periodic or antiperiodic boundary conditio…
We evaluate the two-point function for the electromagnetic field tensor in $(D+1)$-dimensional de Sitter spacetime assuming that the field is prepared in Bunch-Davies vacuum state. This two-point function is used for the investigation of the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor in the presence of a conducting plate. The VEVs are decomposed into the boundary-free and plate-induced parts. For the latter, closed form analytical expressions are given in terms of the hypergeometric function. For $3\leqslant D\leqslant 8$ the plate-induced part in the …
