Emergent unitarity in de Sitter from matrix integrals

TL;DR

This paper investigates de Sitter quantum gravity using Jackiw-Teitelboim gravity, revealing emergent unitarity in the quantum mechanics of the model through matrix integral duality and non-perturbative effects.

Contribution

It demonstrates that the quantum mechanics of 2D de Sitter gravity exhibits emergent unitarity from matrix integrals, highlighting the role of non-perturbative topology-changing processes.

Findings

Evolution acts unitarily on a subspace up to corrections

Emergence of unitarity is linked to eigenvalue level repulsion

Matrix integral duality underpins the model's quantum behavior

Abstract

We study Jackiw-Teitelboim gravity with positive cosmological constant as a model for de Sitter quantum gravity. We focus on the quantum mechanics of the model at past and future infinity. There is a Hilbert space of asymptotic states and an infinite-time evolution operator between the far past and far future. This evolution is not unitary, although we find that it acts unitarily on a subspace up to non-perturbative corrections. These corrections come from processes which involve changes in the spatial topology, including the nucleation of baby universes. There is significant evidence that this 1+1 dimensional model is dual to a 0+0 dimensional matrix integral in the double-scaled limit. So the bulk quantum mechanics, including the Hilbert space and approximately unitary evolution, emerge from a classical integral. We find that this emergence is a robust consequence of the level repulsion of eigenvalues along with the double scaling limit, and so is rather universal in random matrix theory.