On the Imaginary Part of the Effective Action in de Sitter Spacetime with Different Regularization Schemes

Abstract

The imaginary part of the effective action encodes vacuum instability and particle production in the background field. Two standard approaches are commonly used to derive it: the Bogoliubov method and the Green's function method, which are usually expected to agree. However, in de Sitter spacetime they yield different results. We revisit this problem by introducing explicit time and momentum cutoffs in the Green's function representation of the effective action. The apparent discrepancy is found to be due to the different limiting procedures in regularization, which reproduces the Bogoliubov result and the Green's function result respectively. Therefore, the two approaches are understood to be different regularization limits of the same expression, which clarifies the origin of their disagreement.

arXiv commentComments and an appendix is added, no figures, accepted by Phys. Rev. D

References in corpus (15)

• Heat kernel expansion: user's manual
• Conformal Vacua and Entropy in de Sitter Space
• Entanglement from the vacuum
• Heisenberg-Euler Effective Lagrangians : Basics and Extensions
• Schwinger mechanism revisited
• Lecture notes on interacting quantum fields in de Sitter space
• Cosmological Particle Production: A Review
• On the Instability of Global de Sitter Space to Particle Creation
• Real or Imaginary? (On pair creation in de Sitter space)
• Decay of the de Sitter Vacuum
• Propagators in de Sitter space
• Propagators and Gaussian effective actions in various patches of de Sitter space
• Probing the Vacuum Structure of Spacetime
• Relevance of "on" and "off" transitions in quantum pair production experiments
• On (dis)agreement between different methods of calculation of the imaginary part of the effective action in expanding space-times