Narrow Results

The Casimir stress on two parallel plates in a de Sitter background corresponding to different metric signatures and cosmological constants is calculated for massless scalar fields satisfying Robin boundary conditions on the plates. Our calculation shows that for the parallel plates with false vacuum between and true vacuum outside, the total Casimir pressure leads to an attraction of the plates at very early universe.

We calculate the Casimir stress on a spherical shell in a de Sitter background corresponding to different metric signatures and cosmological constants, for massless scalar fields that satisfy Dirichlet boundary conditions on the shell. We show that a contribution appears due to signature change, which leads to late-time expansion of the bubbles in this background.

Emphasizing first the utility of the generalized Fresnel coefficients in the theory of the Casimir effect in planar cavities, we complement our previous discussion of the ordinary Casimir force on and the Casimir stress in a metal (plasma) slab in a planar cavity. We demonstrate strong dependence of the Casimir stress in a thin slab on properties of the bounding medium in the symmetric Lifshitz configuration. Contrary to this, the stress in a thick slab gradually becomes insensitive on external boundary conditions. We also consider the position dependence of the Casimir force on and stress in a thin metal slab in a planar cavity. Whereas the force per unit area on the slab strongly increases when it approaches a mirror the stress in the slab decreases and eventually changes the sign. Generally, the stress decreases with the cavity width and decreasing reflectivity of the mirrors.