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 freetheory 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.

One-loop gravitational wave spectrum in de Sitter spacetime

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Infrared dynamics of massive scalars from the complementary series in de Sitter space

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“…What survives in ∆ 2 D K is coming from subleading contributions to n 2 , κ 2 and κ * 2 . Corrections to ∆ 2 D K are always logarithmic as in (19) and (21), but the coefficients in front of them are different depending on the case when D − 1 − 3 ν is greater or lower than zero.…”

Scale-invariant power spectra from a Weyl-invariant scalar–tensor theory

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