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Closed universes, factorization, and ensemble averaging

Mykhaylo Usatyuk, Ying Zhao

TL;DR

The work analyzes closed universes in holographic quantum gravity, showing that in a single theory factorization enforces a unique Hartle-Hawking closed-universe state whose wavefunction encodes boundary spectral data. Using JT gravity as a concrete model, the authors demonstrate that HH(b) equals Z_H0(b) for a fixed Hamiltonian, with higher-genus wormhole contributions canceled by factorizing deformations; ensemble averaging over Hamiltonians then yields multiple distinct, smooth, semi-classical wavefunctions corresponding to different inputs. Thus, factorization enforces uniqueness in a fixed theory while ensemble averaging recovers a rich cosmological input space and bulk-like semiclassical behavior. The paper also discusses observables, expansion of closed universes, and the status of factorization for finite boundaries, outlining open questions for higher-dimensional holography and potential formulations via Cauchy-slice holography.

Abstract

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.

Closed universes, factorization, and ensemble averaging

TL;DR

The work analyzes closed universes in holographic quantum gravity, showing that in a single theory factorization enforces a unique Hartle-Hawking closed-universe state whose wavefunction encodes boundary spectral data. Using JT gravity as a concrete model, the authors demonstrate that HH(b) equals Z_H0(b) for a fixed Hamiltonian, with higher-genus wormhole contributions canceled by factorizing deformations; ensemble averaging over Hamiltonians then yields multiple distinct, smooth, semi-classical wavefunctions corresponding to different inputs. Thus, factorization enforces uniqueness in a fixed theory while ensemble averaging recovers a rich cosmological input space and bulk-like semiclassical behavior. The paper also discusses observables, expansion of closed universes, and the status of factorization for finite boundaries, outlining open questions for higher-dimensional holography and potential formulations via Cauchy-slice holography.

Abstract

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.
Paper Structure (16 sections, 27 equations, 1 figure)

This paper contains 16 sections, 27 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Factorization and the uniqueness of closed universe state
  3. Preparing states of closed universes
  4. Hartle-Hawking wave function in a single theory
  5. Ensemble averaging
  6. From matrix integrals to closed universes
  7. Review of JT gravity, matrix integral, and a factorizing theory
  8. Closed universes in JT gravity
  9. The unique closed universe wave function in a fixed theory
  10. Ensemble averaging: Going back to JT gravity with smooth wave functions
  11. Discussion
  12. Ensemble averaging.
  13. Observables in closed universes.
  14. Expanding closed universes.
  15. Factorization for finite boundary conditions.
  16. ...and 1 more sections

Figures (1)

  • Figure 2: We plot the Hartle-Hawking wave function $\Psi_{\text{HH}}(b)$ for a typical and an atypical draw of the ensemble of Hamiltonians. At large $b$ the atypical draw better approximates the bulk gravity answer. See footnote \ref{['footnote:resummation']}.