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  • Open Access

Imaginary part of the effective action in de Sitter spacetime with different regularization schemes

Yu Zhou1,* and Hai-Qing Zhang1,2,†

  • 1Center for Gravitational Physics, Department of Space Science, Beihang University, Beijing 100191, China
  • 2Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China

  • *Contact author: YuZhou_@buaa.edu.cn
  • †Contact author: hqzhang@buaa.edu.cn
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Phys. Rev. D 113, 026007 – Published 9 January, 2026

DOI: https://doi.org/10.1103/tpdv-2q6v

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.

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Phys. Rev. D 113, 026007– Published 9 January, 2026
  • Received 22 October 2025
  • Accepted 12 December 2025
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