## 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.

Original language | English |
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Article number | 135019 |

Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Classical and Quantum Gravity |

Volume | 26 |

Issue number | 13 |

DOIs | |

Publication status | Published - 7 Jul 2009 |

## Keywords

- PARTICLE CREATION
- GRAVITON PROPAGATOR
- QUANTUM-FIELDS
- SPACETIME
- STATES