Casimir effect for a spherical shell in de Sitter space

The Casimir stress on a spherical shell in the de Sitter background for a massless scalar field satisfying Dirichlet boundary conditions on the shell is calculated. The metric is written in conformally flat form. Although the metric is time dependent, no particles are created. The Casimir stress is calculated for inside and outside of the shell with different backgrounds corresponding to different cosmological constants. The detailed dynamics of the bubble depends on different parameters of the model. Specifically, bubbles with a true vacuum inside expand if the difference in the Vacuum energies is small, otherwise they collapse.