Perturbative and Non-Perturbative Aspects of Lorentzian Quantum Cosmology

概要

One of the fundamental issues in quantum gravity is how to describe the initial state of the Universe. In quantum cosmology, the quantum state of the entire Universe is formulated as the “wave function of the Universe,” and its origin has been investigated using the path integral approach. However, conventional formulations based on the Euclidean path integral suffer from intrinsic problems.

​In this talk, I will review recent developments in quantum cosmology based on the Lorentzian path integral and introduce our work applying Picard-Lefschetz theory and resurgence theory to this framework. First, I will explain how introducing an infinitesimal deformation in the parameter space fixes the Lefschetz thimble structure, naturally selecting the tunneling wave function. Second, I will demonstrate that the Borel resummation ambiguity of the perturbative series around the saddle is exactly canceled by the non-perturbative contribution from the other saddle. These results illustrate how non-perturbative aspects of quantum gravity offer new perspectives on the origin of the Universe. If time permits, I will also discuss the perturbation issues in quantum cosmology.

---