# Low-dimensional de Sitter quantum gravity

## TL;DR

This paper explores low-dimensional de Sitter quantum gravity, establishing connections with Euclidean AdS gravity, and proposes a genus expansion framework linked to matrix models for a non-perturbative understanding.

## Contribution

It demonstrates that de Sitter JT gravity and pure de Sitter gravity in three dimensions are analytic continuations of their Euclidean AdS counterparts and introduces a genus expansion related to matrix models.

## Key findings

- De Sitter JT gravity is an analytic continuation of Euclidean AdS$_2$ JT gravity.
- Pure de Sitter gravity in three dimensions continues from Euclidean AdS$_3$ gravity.
- A genus expansion for de Sitter JT gravity is proposed, related to matrix models.

## Abstract

We study aspects of Jackiw-Teitelboim (JT) quantum gravity in two-dimensional nearly de Sitter (dS) spacetime, as well as pure de Sitter quantum gravity in three dimensions. These are each theories of boundary modes, which include a reparameterization field on each connected component of the boundary as well as topological degrees of freedom. In two dimensions, the boundary theory is closely related to the Schwarzian path integral, and in three dimensions to the quantization of coadjoint orbits of the Virasoro group. Using these boundary theories we compute loop corrections to the wavefunction of the universe, and investigate gravitational contributions to scattering. Along the way, we show that JT gravity in dS$_2$ is an analytic continuation of JT gravity in Euclidean AdS$_2$, and that pure gravity in dS$_3$ is a continuation of pure gravity in Euclidean AdS$_3$. We define a genus expansion for de Sitter JT gravity by summing over higher genus generalizations of surfaces used in the Hartle-Hawking construction. Assuming a conjecture regarding the volumes of moduli spaces of such surfaces, we find that the de Sitter genus expansion is the continuation of the recently discovered AdS genus expansion. Then both may be understood as coming from the genus expansion of the same double-scaled matrix model, which would provide a non-perturbative completion of de Sitter JT gravity.