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PreprintCC BY 4.0arXiv

Taming the infrared in de Sitter space: autonomous equations, stochastic approach, and Borel resummation

  • Alexander Kamenshchik
  • Polina Petriakova
  • Tereza Vardanyan
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Abstract

We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent functions, and show that these functions approximate the time evolution of the correlation functions of the stochastic theory reasonably well. Second, we apply the technique of autonomous equations to the Borel-Le Roy transforms of correlation functions, and use solutions of these equations to perform Borel resummation. The results match the time evolution obtained in the stochastic picture substantially better. In addition, we propose an alternative method for extracting perturbative coefficients and provide a new derivation of our autonomous equation by truncating a system of Schwinger-Dyson-type differential equations.

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Cite

BibTeXRIS
BibTeX
@misc{kamenshchik2026taming,
  title = {{Taming the infrared in de Sitter space: autonomous equations, stochastic approach, and Borel resummation}},
  author = {Alexander Kamenshchik and Polina Petriakova and Tereza Vardanyan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.09736},
  eprint = {2605.09736},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.09736},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Taming the infrared in de Sitter space: autonomous equations, stochastic approach, and Borel resummation
AU  - Alexander Kamenshchik
AU  - Polina Petriakova
AU  - Tereza Vardanyan
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2605.09736
UR  - https://arxiv.org/abs/2605.09736
AB  - We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent functions, and show that these functions approximate the time evolution of the correlation functions of the stochastic theory reasonably well. Second, we apply the technique of autonomous equations to the Borel-Le Roy transforms of correlation functions, and use solutions of these equations to perform Borel resummation. The results match the time evolution obtained in the stochastic picture substantially better. In addition, we propose an alternative method for extracting perturbative coefficients and provide a new derivation of our autonomous equation by truncating a system of Schwinger-Dyson-type differential equations.
ER  -