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We study conformally-coupled massive scalar field theory with the mass termtreated as a perturbation in the expanding half of de Sitter spacetime as a toymodel for comparing various perturbative formalisms. We point out that thein-out perturbation theory breaks down due to infrared divergences coming fromthe infinite future. We then clarify the relation between the free-theoryvacuum and the true vacuum using the Bogolubov transformation and show that thediscrepancy between the free-theory out-vacuum and the true vacuum causesapparent pair creation of free-theory particles and makes the in-out two-pointfunction differ from the true two-point function. We also identify the infiniteBogolubov coefficients as the cause of infrared divergences. We then examinetwo alternative approaches: the Euclidean and in-in formalisms. We verify thatthere are no infrared divergences in perturbation theory with the mass termtreated as a perturbation in either of these approaches and that the two-pointfunction of massive scalar field is reproduced correctly by these methods.

A conformally coupled massive scalar field in the de Sitter expanding universe with the mass term treated as a perturbation