Closed universes, factorization, and ensemble averaging

We study closed universes in holographic theories of quantum gravity. We argue that within any fixed theory, factorization implies there is one unique closed universe state. The wave function of any state that can be prepared by the path integral is proportional to the Hartle-Hawking wave function. This unique wave function depends on the properties of the underlying holographic theory such as the energy spectrum. We show these properties explicitly in JT gravity, which is known to be dual to an ensemble of random Hamiltonians. For each member of the ensemble, the corresponding wave function is erratic as a result of the spectrum being chaotic. After ensemble averaging, we obtain smooth semi-classical wave functions as well as different closed universe states.