The Wave Function of Quantum de Sitter

TL;DR

This paper computes the Hartle-Hawking wave function for three-dimensional quantum gravity with a positive cosmological constant, revealing non-perturbative instabilities of de Sitter space through exact calculations.

Contribution

It introduces an exact method to compute the wave function of quantum de Sitter space using analytic continuation from Euclidean Anti-de Sitter space, including non-perturbative effects.

Findings

Wave function is non-normalizable and peaked at inhomogeneous geometries.

Identifies a non-perturbative instability of three-dimensional de Sitter space.

Provides a framework for exact quantum gravity calculations in de Sitter space.

Abstract

We consider quantum general relativity in three dimensions with a positive cosmological constant. The Hartle-Hawking wave function is computed as a function of metric data at asymptotic future infinity. The analytic continuation from Euclidean Anti-de Sitter space provides a natural integration contour in the space of metrics, allowing us -- with certain assumptions -- to compute the wave function exactly, including both perturbative and non-perturbative effects. The resulting wave function is a non-normalizable function of the conformal structure of future infinity which is infinitely peaked at geometries where I^+ becomes infinitely inhomogeneous. We interpret this as a non-perturbative instability of de Sitter space in three dimensional Einstein gravity.