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

Abstract

We study conformally coupled massive scalar field theory with the mass term treated as a perturbation in the expanding half of de Sitter spacetime as a toy model for comparing various perturbative formalisms. We point out that the in–out perturbation theory breaks down due to infrared divergences coming from the infinite future. We then clarify the relation between the free-theory vacuum and the true vacuum using the Bogolubov transformation and show that the discrepancy between the free-theory out-vacuum and the true vacuum causes apparent pair creation of free-theory particles and makes the in–out two-point function differ from the true two-point function. We also identify the infinite Bogolubov coefficients as the cause of infrared divergences. We then examine two alternative approaches: the Euclidean and in–in formalisms. We verify that there are no infrared divergences in perturbation theory with the mass term treated as a perturbation in either of these approaches and that the two-point function of the massive scalar field is reproduced correctly by these methods.