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.

arXiv comment43 pages, 38 figures