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Casimir stress on parallel plates in a de Sitter space

The Casimir stress on two parallel plates in a de Sitter background for a 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. We have also considered the case of different cosmological constants for the space between and outside of the plates to make it applicable to the case of domain wall formations in the early universe.