Krein Space Quantization of Casimir Effect for a Spherical Shell

The Casimir stress on a spherical shell in de Sitter spacetime for a massless scalar field is calculated using Krein space quantization. In this method, the auxiliary negative frequency states have been utilized, the modes of which do not interact with the physical states and are not affected by the physical boundary conditions. These unphysical states just play the role of an automatic renormalization tool for the theory.