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 massive scalar field is reproduced correctly by these methods.

15 pages

References in corpus (6)

• Quantum Contributions to Cosmological Correlations
• De Sitter Space and Eternity
• Particle decay during inflation: self-decay of inflaton quantum fluctuations during slow roll
• Particle decay in inflationary cosmology
• Decay of the free-theory vacuum of scalar field theory in de Sitter spacetime in the interaction picture
• How to use retarded Green's functions in de Sitter spacetime

Cited by in corpus (16)

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• Infrared dynamics of massive scalars from the complementary series in de Sitter space
• The IR stability of de Sitter QFT: Physical initial conditions
• Classical radiation by free-falling charges in de Sitter spacetime
• Quantum corrections to the gravitational potentials of a point source due to conformal fields in de Sitter
• de Sitter Space is Unstable in Quantum Gravity
• Quantum corrections for spinning particles in de Sitter
• Our Universe from the cosmological constant
• Isometry invariance of exact correlation functions in various charts of Minkowski and de Sitter spaces
• Scale-invariant spectrum of Lee-Wick model in de Sitter spacetime
• Scale-invariant power spectra from a Weyl-invariant scalar-tensor theory
• Scale-invariant scalar spectrum from the nonminimal derivative coupling with fourth-order term