Jackiw-Teitelboim Gravity and Lorentzian Quantum Cosmology

TL;DR

This paper evaluates probability amplitudes in Jackiw-Teitelboim gravity using Lorentzian path integrals, revealing insights into quantum cosmology, boundary conditions, and universe genesis in two-dimensional models.

Contribution

It provides a detailed Lorentzian path integral analysis of JT gravity, including boundary conditions, saddle points, and the quantum genesis of the universe, with implications for quantum cosmology.

Findings

Amplitude expressed via modified Bessel function of the second kind.

Hartle-Hawking no-boundary proposal is approximately valid in JT quantum cosmology.

Quantum genesis occurs with perturbative regularity when the dilaton is large and positive.

Abstract

We directly evaluate the probability amplitudes in Jackiw-Teitelboim (JT) gravity using the Lorentzian path integral formulation. By imposing boundary conditions on the scale factor and the dilaton field, the Lorentzian path integral uniquely yields the probability amplitude without contradiction. Under Dirichlet boundary conditions, we demonstrate that the amplitude derived from the Lorentzian path integral is expressed in terms of the modified Bessel function of the second kind. Furthermore, we provide the determinant for various boundary conditions and perform a detailed analysis of the Lefschetz thimble structure and saddle points. In contrast to four-dimensional gravity, we show that the Hartle-Hawking no-boundary proposal is approximately valid in JT quantum cosmology. Furthermore, addressing quantum perturbation issues, we show that the quantum genesis of the two-dimensional universe occurs and exhibits perturbative regularity when the dilaton field is non-zero and large as an initial condition.