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

TY - JOUR

T1 - A conformally coupled massive scalar field in the de Sitter expanding universe with the mass term treated as a perturbation

AU - Higuchi, Atsushi

AU - Cheong, Lee Yen

PY - 2009/7/7

Y1 - 2009/7/7

N2 - 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.

AB - 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.

KW - PARTICLE CREATION

KW - GRAVITON PROPAGATOR

KW - QUANTUM-FIELDS

KW - SPACETIME

KW - STATES

UR - http://www.scopus.com/inward/record.url?scp=67649749176&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/26/13/135019

DO - 10.1088/0264-9381/26/13/135019

M3 - Article

SN - 1361-6382

VL - 26

SP - 1

EP - 14

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 13

M1 - 135019

ER -