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

Emergent unitarity in de Sitter from matrix integrals