Jackiw-Teitelboim and Kantowski-Sachs quantum cosmology

TL;DR

This paper explores quantum cosmology in 2D Jackiw-Teitelboim gravity with positive cosmological constant, establishing a correspondence with Kantowski-Sachs models to compute the Hartle-Hawking wave function and analyze the probability distribution of the dilaton field.

Contribution

It introduces a novel JT-KS correspondence that enables the calculation of the Hartle-Hawking wave function in JT gravity using path integrals and Picard-Lefschetz theory.

Findings

Derived the Hartle-Hawking wave function for JT gravity.

Established a mapping between JT and Kantowski-Sachs models.

Provided a probability distribution for the dilaton field.

Abstract

We study quantum cosmology of the $2D$ Jackiw-Teitelboim (JT) gravity with $\Lambda>0$ and calculate the Hartle-Hawking (HH) wave function for this model in the minisuperspace framework. Our approach is guided by the observation that the JT dynamics can be mapped exactly onto that of the Kantowski-Sachs (KS) model describing a homogeneous universe with spatial sections of $S^1\times S^2$ topology. This allows us to establish a JT-KS correspondence between the wave functions of the models. We obtain the semiclassical Hartle-Hawking wave function by evaluating the path integral with appropriate boundary conditions and employing the methods of Picard-Lefschetz theory. The JT-KS connection formulas allow us to translate this result to JT gravity, define the HH wave function and obtain a probability distribution for the dilaton field.