A quantum field theory of a charged scalar field with self-interactions in a Robertson-Walker metric is considered. The structure of the Hilbert space of the state vectors in this theory is investigated; and taking account of the change of the Fock space, a method of calculating physical quantities is constructed and its diagrammatic version is given. By practical calculation to second order in the coupling constant, it is shown that the theory is renormalizable and renormalization constants are identical to those in the theory in Minkowski spacetime.
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Ikuo Ichinose (1982) studied this question.
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