Emergent unitarity in de Sitter from matrix integrals

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.

Automated summary

In this study, the Jackiw-Teitelboim gravity model with positive cosmological constant is examined as a model for de Sitter quantum gravity, focusing on quantum mechanics at past and future infinity. The research reveals an infinite-time evolution operator that acts unitarily on a subspace up to non-perturbative corrections due to spatial topology changes. This 1+1 dimensional model is suggested to be dual to a 0+0 dimensional matrix integral in the double-scaled limit, indicating the emergence of bulk quantum mechanics from classical integrals.