Casimir effect for parallel plates in a Friedmann-Robertson-Walker universe

Abstract

We evaluate the Hadamard function, the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a massive scalar field with general curvature coupling parameter in the geometry of two parallel plates on a spatially flat Friedmann-Robertson-Walker background with a general scale factor. On the plates, the field operator obeys the Robin boundary conditions with the coefficients depending on the scale factor. In all the spatial regions, the VEVs are decomposed into the boundary-free and boundaryinduced contributions. Unlike to the problem with the Minkowski bulk, in the region between the plates the normal stress is not homogeneous and does not vanish in the geometry of a single plate. Near the plates, it has different signs for accelerated and deccelerated expansions of the universe. The VEV of the energy-momentum tensor, in addition to the diagonal components, has a nonzero off-diagonal component describing an energy flux along the direction normal to the boundaries. Expressions are derived for the Casimir forces acting on the plates. Depending on the Robin coefficients and on the vacuum state, these forces can be either attractive or repulsive. An important difference from the corresponding result in the Minkowski bulk is that the forces on the separate plates, in general, are different if the corresponding Robin coefficients differ. We give the applications of general results for the class of α-vacua in the de Sitter bulk. It is shown that, compared with the Bunch-Davies vacuum state, the Casimir forces for a given α-vacuum may change the sign.

Remarks on Some Results Related to the Thermal Casimir Effect in Einstein and Closed Friedmann Universes with a Cosmic String

“…valid for bosons and fermions, respectively. In both cases, the function Φ(t) in Equations (31) and (32) have the same form as E (s)…”

“…After the publication of the pioneering papers by Ford [21,25], Dowker and Critchley [22], Mamayev, Mostepanneko and Starobinsky [23], the Casimir effect was investigated in different cosmological scenarios. Among the papers devoted to this subject, we can mention the ones by Bellucci and Saharian [28], Saharian and Mkhitaryan [29], Pavlov [30], Altaie [31] and Bezerra de Mello, Saharian and Setare [32]. Also some discussions concerning the Casimir effect in multi-dimensional cosmology [33] and the problem of dark energy [34] were presented.…”

Canonical relativistic formulation to calculate the Casimir force four-vector on anisotropic conductor polarizable and magnetizable media

“…for each wave vector k. Substituting (12) and (13) in the definitions of the electric-magnetic polarization tensor and the free electric current density four-vector given by (9) and (10), the relativistic covariant constitutive relations of the anisotropic conductor polarizable and magnetizable medium are obtained as 74 which relate the antisymmetric electric-magnetic polarization tensor and the free electric current density four-vector, induced in the anisotropic conductor polarizable and magnetizable medium, to the strength tensor of the electromagnetic field…”

“…The Casimir force has been discussed widely in many area of physics such as atomic physics, [1][2][3][4] gravitation and cosmology, [5][6][7][8][9][10][11][12][13][14][15] high energy physics [16][17][18][19][20][21][22][23] and condensed matter physics. [24][25][26][27] In quantum electrodynamics, the Casimir force is one of the consequences of the quantization of electromagnetic field in the presence of absorbing media.…”

Casimir effect in Snyder Space

“…More important to us are its applications to theories Beyond the Standard Model (BSM), which run from the consideration of the effect in curved spaces [12,13] to the possible implications on neutrino oscillations [14] or more general scenarios like brane-worlds, extra dimensions, scale-invariant models and generalized uncertainty principle [15,16,17]. From the experimental side, many constraints related to possible modifications of Newtonian gravity have been obtained [18] in the last decades; the latest results fix for example stringent bounds to the axion mass and coupling [19].…”