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

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

2009-03-23

arxiv.org/abs/0903.3881v2

Class. Quantum Grav. 26 135019 (2009)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages

Scientific paper

10.1088/0264-9381/26/13/135019

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 massive scalar field is reproduced correctly by these methods.

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