The Krein–Gupta–Bleuler quantization in de Sitter space–time; Casimir energy–momentum tensor for a curved brane

In this paper, vacuum expectation value (VEV) of the energy–momentum tensor for a conformally coupled scalar field in de Sitter space–time is investigated through the Krein–Gupta–Bleuler construction. This construction has already been successfully applied to the de Sitter minimally coupled massless scalar field and massless spin-2 field to obtain a causal and fully covariant quantum field on de Sitter background. We also consider the effects of boundary conditions. In this respect, Casimir energy–momentum tensor induced by Dirichlet boundary condition on a curved brane is evaluated.