The Baby Universe is Fine and the CFT Knows It: On Holography for Closed Universes

TL;DR

The paper develops a holographic framework for closed universes embedded in AdS/CFT, showing that a large bulk entanglement can encode the entire closed universe in the boundary CFT, while also clarifying the interpretation of a seemingly paradoxical one-dimensional closed-universe Hilbert space. It introduces an intrinsic dictionary linking final-state data to CFT observables, and demonstrates how conventional gravitational EFT emerges via coarse-graining over microscopic final states. By deploying a tensor-network/MERA toy model and ETH-inspired ensembles, the authors analyze regimes from approximately isometric to highly non-isometric encodings, and address SWAP-test debates to defend the semiclassical description of bulk physics within the closed universe. The work also connects observer-related questions to holography, proposes arrow-of-time mechanisms, and outlines how QFT on the closed universe can be reconstructed from CFT data through operational CFT experiments. Overall, the results advocate a healthy, testable holographic picture for baby universes born from AdS/CFT, with clear paths to broader cosmological applications and future refinements of gravitational EFT in closed cosmologies.

Abstract

Big bang/big crunch closed universes can be realized in AdS/CFT, even though they lack asymptotically AdS boundaries. With enough bulk entanglement, the bulk Hilbert space of a closed universe can be holographically encoded in the CFT. We clarify the relation of this encoding to observer-clone proposals and refute recent arguments about the breakdown of semiclassical physics in such spaces. In the limit of no bulk entanglement, the holographic encoding breaks down. The oft-cited one-dimensional nature of the closed universe Hilbert space represents the limitation of the external (CFT) Hilbert space to access the quantum information in the closed universe, similar to the limitations imposed on observers outside a perfectly isolated quantum lab. We advocate that the CFT nevertheless continues to determine the physical properties of the closed universe in this regime, showing how to interpret this relationship in terms of a final state projection in the closed universe. We provide a dictionary between the final state wavefunction and CFT data. We propose a model of the emergence of an arrow of time in the universe with a given initial or final state projection. Finally, we show that the conventional EFT in the closed universe, without any projection, can be recovered as a maximally ignorant description of the final state. This conventional EFT is encoded in CFT data, and it can be probed by computing coarse-grained observables. We provide an example of one such observable. Taken together, these results amount to a clean bill of health for baby universes born of AdS/CFT.

Figures (23)

• Figure 1: On the left, representation of the semiclassical state on the time-symmetric slice. The lines connecting $\mathsf{l},\mathsf{r}$ and $\mathsf{c}$ correspond to entanglement lines of matter. On the right, Penrose diagram of the spacetime, where each point represents a sphere $\mathbf{S}^{d-1}$. The dashed line is the time-symmetric slice. The thin black lines are $r=0$ where the spheres cap off smoothly.
• Figure 2: Tensor network model in Antonini:2023hdh for the microstate.
• Figure 3: AdS-local tensor network model of the closed universe state $\ket{\mathcal{O}_{\mathsf{c}}}$ in the bulk Hilbert space. The tensor network is constructed from two MERA codes with large bond dimension, glued at a finite radius $R_*$ with the insertion of the shell operator (red). In section \ref{['sec:intrinsic']} we will interpret this state as the initial/final state of the closed universe.
• Figure 4: On the left, Euclidean CFT path integral on $\mathbf{R}\times \mathbf{S}^{d-1}$ which prepares the microstate. On the right, the leading Euclidean gravitational solution which prepares the semiclassical state. Neglecting the backreaction of matter except for the heavy shell, the manifold is composed of two Euclidean AdS spaces (EAdS), cut and glued across the trajectory of the shell.
• Figure 5: The Euclidean wormhole reproducing the variance of the norm of the microstate over an ensemble of Gaussian microscopic thin shell operators. The boundary vertical black lines connect the bra and ket contours in the CFT Hilbert spaces, where all of the microscopic states live. For a detailed construction of this wormhole, see Antonini:2023hdh.