Dimensional (In)dependence of Lorentzian Quantum Cosmology
Abstract
We study transition amplitudes of the quantum universe in D-dimensional spacetime within the de Sitter minisuperspace approximation in Einstein gravity. Using the Lorentzian path integral combined with Picard-Lefschetz theory, we identify the saddle points that contribute to the integral and derive a well-defined transition amplitude under Dirichlet boundary conditions. We further show numerically that a resurgence analysis based on Borel-Padé resummation is effective in resolving the residual Stokes ambiguities that arise in certain cases. Analyzing three-, four-, and five-dimensional cases, as well as the large-D limit, we find that the tunneling proposal is commonly realized for the creation of the universe from nothing. This result implies a universal feature of quantum cosmology based on Einstein gravity across dimensions.
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BibTeX
@misc{honda2026dimensional,
title = {{Dimensional (In)dependence of Lorentzian Quantum Cosmology}},
author = {Masazumi Honda and Hiroki Matsui and Kota Numajiri and Kazumasa Okabayashi and Takahiro Terada},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33452},
eprint = {2609.33452},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33452},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dimensional (In)dependence of Lorentzian Quantum Cosmology
AU - Masazumi Honda
AU - Hiroki Matsui
AU - Kota Numajiri
AU - Kazumasa Okabayashi
AU - Takahiro Terada
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33452
UR - https://arxiv.org/abs/2609.33452
AB - We study transition amplitudes of the quantum universe in D-dimensional spacetime within the de Sitter minisuperspace approximation in Einstein gravity. Using the Lorentzian path integral combined with Picard-Lefschetz theory, we identify the saddle points that contribute to the integral and derive a well-defined transition amplitude under Dirichlet boundary conditions. We further show numerically that a resurgence analysis based on Borel-Padé resummation is effective in resolving the residual Stokes ambiguities that arise in certain cases. Analyzing three-, four-, and five-dimensional cases, as well as the large-D limit, we find that the tunneling proposal is commonly realized for the creation of the universe from nothing. This result implies a universal feature of quantum cosmology based on Einstein gravity across dimensions.
ER -