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Cited by 35Black Holes and Theoretical PhysicsNoncommutative and Quantum Gravity TheoriesCosmology and Gravitation Theories

The DOI matches its Crossref record; 146 of the 146 references it cites were found in a registry or an index; 2 of the 100 sources its claims cite were checked for support.

The baby universe is fine and the CFT knows it: on holography for closed universes

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Antonini, Stefano, Rath, Pratik, Sasieta, Martin, Swingle, Brian, Vilar López, Alejandro·2025·Journal of High Energy Physics
DOI 10.1007/jhep12(2025)159
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Abstract

A bstract: 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. A video abstract is available at https://youtu.be/s_9VqF-N8uQ .

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TL;DR

The paper revisits the AS2 construction of big-bang/big-crunch closed universes in AdS/CFT and argues that a large closed universe can remain semiclassical even when its Hilbert space appears one-dimensional from the CFT. It refutes a recent SWAP-test argument against semiclassicality, proposes a final-state-projection dictionary between the closed-universe wavefunction and CFT data, and shows conventional closed-universe EFT can be recovered by coarse-graining over final states.

Key findings

  • In the AS2 model, bulk entanglement between the closed universe and AdS regions can be large. In AdS₅×S⁵, the AdS gas entropy is \(S(lr)=(E\ell)^{9/10}\), allowed up to \(E\ell \lesssim O(N^{20/17})\), with \(S(lr)=O(N^{18/17})\) at the transition; the closed-universe entropy is \(S(c)=(m\ell)^2 N^{50/17}\) for \(O(N^2/\lambda^{1/2}) \ll m\ell \ll O(N^2)\), and \(S(c)=m\ell\, N^{16/17}\) for \(O(N^2) \ll m\ell\). The holographic encoding is approximately isometric when \(4S(lr)-3S(c)\gg 1\), effectively isometric when \(S(lr)\gg \log S(c)\), highly non-isometric when \(S(lr)\lesssim \log S(c)\), and breaks down at zero entanglement.
  • The EG SWAP test is argued to reduce to the boundary SWAP; for a pure CFT state its expectation value is unity, so it cannot distinguish whether a closed universe is present. The one-dimensional closed-universe Hilbert space is interpreted as the external CFT’s inability to access the closed universe, not as a breakdown of semiclassical physics inside it.
  • The paper proposes a final-state projection picture: the CFT determines the final state \(|O_c\rangle\) via the dictionary “final state wavefunction \(\leftrightarrow\) CFT light-light matrix elements of the heavy shell operator \(O\),” \(\Psi_I^O=O_I\). ETH makes this final state quasi-random; averaging over final states gives the maximally mixed \(\rho=\frac{1}{d_c}\mathbb{1}_c\), recovering conventional EFT, while independent replica averaging gives \(\mathrm{rank}(\rho)=d_c\) and correlated averaging gives \(\mathrm{rank}(\rho)=1\).
  • CFT experiments can probe closed-universe geometry even at zero entanglement. For example, a two-point function is \(G(\alpha)=e^{-m_A L(\alpha)}\), with \(L(\alpha)=2\ell\log[2\sinh((\alpha+\Delta\tau)/\ell)]\) and \(r_0=\ell\sinh((\alpha+\Delta\tau)/\ell)\); an arrow-of-time toy model yields a Schrödinger-cat-like ground state with eigenvalues \(E_{--}(1\pm|\zeta|+\cdots)\).

Methods

  • Reviews and expands the AS2 semiclassical state: two asymptotically AdS regions plus a closed universe supported by a thin dust shell, prepared by Euclidean CFT path integrals/PETS and analyzed via gravitational path-integral saddles and wormholes.
  • Uses a random tensor network/MERA model of the holographic map \(W\), Marchenko-Pastur eigenvalue statistics for \(W^\dagger W\), and an ETH ensemble of heavy operators to compute overlaps, variances, Hilbert-space dimensions, and coarse-grained final states.
  • Proposes CFT protocols with heralded controlled operations and Euclidean evolution to measure matrix elements and reconstruct bulk geometry; includes a canonical quantum gravity argument and numerical exact diagonalization for the arrow-of-time toy model.

Limitations

  • Stated: the authors do not claim AdS/CFT will be essential or even useful for describing closed universes in general; the tensor network leaves out details of a full holographic CFT; the Appendix C canonical quantum gravity derivation sweeps many issues under the rug; it is unclear whether local physics from a pure initial/final decoherence functional recovers standard quantum mechanics; complexity limitations are ignored in the proposed CFT experiments; the ETH ansatz for light-light matrix elements lies beyond conventional ETH, with evidence mainly from 2D CFTs and gravity.
  • Evident: the results rely on the specific AS2 construction, the heavy-shell limit, Gaussian random tensor/ETH assumptions, and AdS/CFT; no full UV completion or general treatment of arbitrary cosmological singularities is provided.

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Cites

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Figures

Figure 1 On the left, representation of the semiclassical state on the time-symmetric slice. The lines connecting l , r and c correspond to entanglement lines of matter. On the right, Penrose diagram of the spacetime, where each point represents a sphere 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 1 On the left, representation of the semiclassical state on the time-symmetric slice. The lines connecting l , r and c correspond to entanglement lines of matter. On the right, Penrose diagram of the spacetime, where each point represents a sphere S d ´ 1 . The dashed line is the time-symmetric slice. The thin black lines are r ' 0 where the spheres cap off smoothly.CC-BY · From the PDF
Figure 2 Tensor network model in [6] for the microstate.
Figure 2 Tensor network model in [6] for the microstate.CC-BY · From the PDF
Figure 3 AdS-local tensor network model of the closed universe state |O c y 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 4 we will interpret this state as the initial/final state of the closed universe.
Figure 3 AdS-local tensor network model of the closed universe state |O c y 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 4 we will interpret this state as the initial/final state of the closed universe.CC-BY · From the PDF
Figure 4 On the left, Euclidean CFT path integral on R ˆ 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 4 On the left, Euclidean CFT path integral on R ˆ 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.CC-BY · From the PDF
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 [6].
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 [6].CC-BY · From the PDF
Figure 6 Parameter space of the semiclassical states in AdS 5 ˆ S 5 .
Figure 6 Parameter space of the semiclassical states in AdS 5 ˆ S 5 .CC-BY · From the PDF
Figure 7 The holographic encoding of the closed universe W is defined through the fixed Ob -lr bulk entanglement.
Figure 7 The holographic encoding of the closed universe W is defined through the fixed Ob -lr bulk entanglement.CC-BY · From the PDF
Figure 8 Left : Two representations of the bulk saddle computing x Ψ j | Ψ i y . The blue line is the (dominant) matter geodesic and the red line pinches off in the heavy shell limit. The bottom diagram is more like those used to discuss closed cosmologies. Notice that the 'past' and 'future' boundaries (or 'bra' and 'ket') are not disconnected due to the external regions connecting to the CFT: this plays a similar role to the observer lines in [52]. Right : Two-boundary wormhole computing the square of the overlap. The front face gives Tr p ρ 2 l q , the back computes Tr p ρ 2 r q . This reflects how the external observer-like lines connect between copies through the bulk.
Figure 8 Left : Two representations of the bulk saddle computing x Ψ j | Ψ i y . The blue line is the (dominant) matter geodesic and the red line pinches off in the heavy shell limit. The bottom diagram is more like those used to discuss closed cosmologies. Notice that the 'past' and 'future' boundaries (or 'bra' and 'ket') are not disconnected due to the external regions connecting to the CFT: this plays a similar role to the observer lines in [52]. Right : Two-boundary wormhole computing the square of the overlap. The front face gives Tr p ρ 2 l q , the back computes Tr p ρ 2 r q . This reflects how the external observer-like lines connect between copies through the bulk.CC-BY · From the PDF
Figure 9 On the left, Description 2 consists of a pure state on the lr AdS spaces. On the right, tensor network model of the CFT state. The closed universe tensor has been absorbed into the state of the quantum fields.
Figure 9 On the left, Description 2 consists of a pure state on the lr AdS spaces. On the right, tensor network model of the CFT state. The closed universe tensor has been absorbed into the state of the quantum fields.CC-BY · From the PDF
Figure 10 The causal wedge SWAP operator S LR as defined in [60] also swaps the closed universes and has unit expectation value.
Figure 10 The causal wedge SWAP operator S LR as defined in [60] also swaps the closed universes and has unit expectation value.CC-BY · From the PDF
Figure 11 If the cl entanglement is sufficiently large, the partial CFT SWAP S R does not swap the closed universe and detects the bulk entanglement to the r AdS space.
Figure 11 If the cl entanglement is sufficiently large, the partial CFT SWAP S R does not swap the closed universe and detects the bulk entanglement to the r AdS space.CC-BY · From the PDF
Figure 12 On the left, the Euclidean CFT path integral that prepares this state. The blue boundaries represent a fixed low-energy input state, which could e.g. be the CFT ground state. On the right, the bulk saddle point preparing the semiclassical unentangled state, represented in a way to make contact with Figure 4.
Figure 12 On the left, the Euclidean CFT path integral that prepares this state. The blue boundaries represent a fixed low-energy input state, which could e.g. be the CFT ground state. On the right, the bulk saddle point preparing the semiclassical unentangled state, represented in a way to make contact with Figure 4.CC-BY · From the PDF
Figure 13 On the left, the big bang / big crunch singularity implements an initial / final state projection compatible with each other. Both states propagate to |O c y at the time-symmetric slice. On the right, the holographic map. The universe is prepared in an entangled state with lr . The final state projection generates a backflow of quantum information from the singularity to Ob , which finally reaches lr through the bulk entanglement.
Figure 13 On the left, the big bang / big crunch singularity implements an initial / final state projection compatible with each other. Both states propagate to |O c y at the time-symmetric slice. On the right, the holographic map. The universe is prepared in an entangled state with lr . The final state projection generates a backflow of quantum information from the singularity to Ob , which finally reaches lr through the bulk entanglement.CC-BY · From the PDF
Figure 14 The matrix elements define closed universe tensor networks. On the left, the closed universe tensor network computing the vacuum expectation value O 00 ' x 0 | O | 0 y of the shell operator. On the right, the closed universe tensor network computing the matrix element O I ' x Ψ i 1 | O | Ψ i y between two excited gas states | Ψ i y (blue) and | Ψ i 1 y (green). These numbers determine the wavefunction of the closed universe final state |O c y represented in Figure 3.
Figure 14 The matrix elements define closed universe tensor networks. On the left, the closed universe tensor network computing the vacuum expectation value O 00 ' x 0 | O | 0 y of the shell operator. On the right, the closed universe tensor network computing the matrix element O I ' x Ψ i 1 | O | Ψ i y between two excited gas states | Ψ i y (blue) and | Ψ i 1 y (green). These numbers determine the wavefunction of the closed universe final state |O c y represented in Figure 3.CC-BY · From the PDF
Figure 15 The statistical average over final states generates the wormhole and prepares the bulk state | ψ I y at the time-symmetric slice when I ' J . The dashed line on the left represents the final state projection.
Figure 15 The statistical average over final states generates the wormhole and prepares the bulk state | ψ I y at the time-symmetric slice when I ' J . The dashed line on the left represents the final state projection.CC-BY · From the PDF
Figure 16 Inter-replica correlated saddle point of the gravitational path integral.
Figure 16 Inter-replica correlated saddle point of the gravitational path integral.CC-BY · From the PDF
Figure 17 Boundary correlation function G p α, α q , with α fi xed and β L , β R Ñ8 .
Figure 17 Boundary correlation function G p α, α q , with α fi xed and β L , β R Ñ8 .CC-BY · From the PDF
Figure 18 The saddle contributing to the two-point function. The on-shell gravitational action of the saddle yields a constant which cancels with the normalization of the state. The relevant quantity for the two-point function is the length of the blue geodesic L p α q .
Figure 18 The saddle contributing to the two-point function. The on-shell gravitational action of the saddle yields a constant which cancels with the normalization of the state. The relevant quantity for the two-point function is the length of the blue geodesic L p α q .CC-BY · From the PDF
Figure 19 Left: the MERA computing the expectation value of the heavy shell operator, made out of primaries (red dots) with scaling dimension ∆ inserted every 2 b sites in the outer layer of the MERA, which has 2 a sites. Right: Contracting the outermost layer of the MERA, the operator insertions are renormalized by a factor of 2 ´ ∆ and the number of sites in the outermost layer of the MERA is cut in half.
Figure 19 Left: the MERA computing the expectation value of the heavy shell operator, made out of primaries (red dots) with scaling dimension ∆ inserted every 2 b sites in the outer layer of the MERA, which has 2 a sites. Right: Contracting the outermost layer of the MERA, the operator insertions are renormalized by a factor of 2 ´ ∆ and the number of sites in the outermost layer of the MERA is cut in half.CC-BY · From the PDF
Figure 20 Left : Euclidean preparation and Lorentzian evolution of the two-shell states with a bottleneck. Right : Geometry of the time-reflection symmetric slice.
Figure 20 Left : Euclidean preparation and Lorentzian evolution of the two-shell states with a bottleneck. Right : Geometry of the time-reflection symmetric slice.CC-BY · From the PDF
Figure 21 Saddle computing the overlap G ji .
Figure 21 Saddle computing the overlap G ji .CC-BY · From the PDF
Figure 22 The three two-boundary wormholes contributing to (B.3). The blue geodesics have always the same length in the heavy shell limit in which the red shells pinch off.
Figure 22 The three two-boundary wormholes contributing to (B.3). The blue geodesics have always the same length in the heavy shell limit in which the red shells pinch off.CC-BY · From the PDF
Figure 23 On the left, the closed universe final state wavefunction for a large universe can be defined in terms of the matrix elements of the heavy matter operator computed by the CFT path integral. On the right, the wavefunction can be extended to the closed universes of this paper in the heavy shell limit, where the heavy matter operator stays in the asymptotic region.
Figure 23 On the left, the closed universe final state wavefunction for a large universe can be defined in terms of the matrix elements of the heavy matter operator computed by the CFT path integral. On the right, the wavefunction can be extended to the closed universes of this paper in the heavy shell limit, where the heavy matter operator stays in the asymptotic region.CC-BY · From the PDF

Verification

Claims the paper makes

189 Own interpretation · 104 No basis given · 46 Not checked yet · 18 Sources not found · 6 Check pending · 6 Own result · 2 No full text of the sources · 1 Partly supported · 1 Own method · accuracy not yet measured

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  • It may state two separate claims as one. 116
  • Probably not a substantial claim. 58
  • The quote only partly states this claim. 13
168 of 168

  • The authors state this as an assumption.

    The states |Ψ_AB> and |Ψ'_CD> can be prepared by suitable Euclidean CFT path integrals on a cylinder.

    “We will assume that the states |Ψ AB y and |Ψ 1 CD y can be prepared by suitable Euclidean CFT path integrals on a cylinder, generally via a time-dependent Hamiltonian evolution.”

  • The authors state this as an assumption.

    The mass of each dust particle is small enough (Δ << N^2) that the backreaction on the S5 factor is negligible.

    “we can assume that the mass of each dust particle is small enough, ∆ !N 2 , so that the backreaction on the S 5 factor is negligible.”

  • The paper relies on this without support.

    The AdS part of the metric on the closed universe is determined by (2.1) and (2.2), neglecting the backreaction of other matter fields except for the shell.

    “The AdS part of the metric on the closed universe is then determined by (2.1) and (2.2), again neglecting the backreaction of other matter fields except for the shell.”

  • The authors state this as an assumption.

    The universe can accommodate N^{18/17} matter degrees of freedom per AdS scale volume, defining the code subspace within the closed universe.

    “we will assume that the universe can accommodate N 18{17 matter degrees of freedom per AdS scale volume; this defines our code subspace within the closed universe.”

  • The authors state this as an assumption.

    The heavy shell is not part of the code subspace but is part of a fixed background that holds the universe together.

    “we will not consider the heavy shell as a part of this code subspace, but rather as part of a fixed background which holds the universe together.”

  • The paper relies on this without support.

    The standard holographic dictionary and holographic map V apply to the closed universe setup.

    “Using the standard holographic map V , this bulk operator maps to the boundary SWAP operator, or more precisely to the boundary SWAP operator restricted to a low-energy subspace (although the full SWAP does the job just fine).”

  • The paper relies on this without support.

    The tensor network model used faithfully represents the relevant CFT/closed universe physics.

    “The tensor network makes it clear that the same underlying structure is present in all these cases.”

  • The paper relies on this without support.

    The final state projection perspective is a valid model of the closed universe.

    “Taking this perspective, the final state projection modifies the global structure of the quantum mechanics in the closed universe, irrespective of whether there is entanglement with the exterior or not.”

  • The paper relies on this without support.

    In gravitating systems, fine-grained entropies of microscopic systems can be captured in terms of coarse-grained entropies of dynamically determined regions of the geometry.

    “One of the central lessons of recent years is that, in gravitating systems, fine-grained entropies of”

  • The authors state this as an assumption.

    The erratic parts of the heavy operator's matrix elements behave as i.i.d. random complex Gaussian variables.

    “The erratic parts behave as i.i.d.random complex Gaussian variables, which leads to”

  • The authors state this as an assumption.

    The system Hamiltonian H is a random GOE matrix.

    “The system has a Hilbert space of dimension D S and a Hamiltonian H which we will take to be random and of GOE form.”

  • The authors state this as an assumption.

    The CR action is trivial.

    “Such a GOE Hamiltonian is a simple model of a CRT-invariant bulk theory where we take the CR action to be trivial.”

  • The authors state this as an assumption.

    The system and clock are non-interacting.

    “Although we have idealized the system and clock as not interacting, this is not strictly necessary”

  • The authors state this as an assumption.

    There is a tunable parameter on the states |Ψ_LB> and |Ψ_CR> in (2.5) that changes their energy, and above the threshold these states correspond to high-energy equilibrium states of two-sided small black holes with connected interiors.

    “We assume that there is a tunable parameter on the states |Ψ LB y and |Ψ CR y in (2.5) that changes their energy.Above the threshold, these states correspond to high-energy equilibrium states of two-sided small black holes with connected interiors.”

  • The authors state this as an assumption.

    The Born rule is included in the rules of quantum theory.

    “For now, we are including the Born rule in the rules of quantum theory.”

  • The authors state this as an assumption.

    The observer's Hilbert space H_Ob has smaller dimension than the rest of the universe H_M, i.e., we are in the effectively isometric encoding regime discussed in Section 2.5.

    “Here we assume that the observer's Hilbert space H Ob has smaller dimension than the rest of the universe H M , namely, that we are in the effectively isometric encoding regime discussed in Section 2.5.”

  • The authors state this as an assumption.

    The ground state has a MERA representation.

    “To start, assume, as in [63], that the ground state has a MERA representation, as shown schematically in Figure 19.”

  • The authors state this as an assumption.

    Z(2β_N) is also in the black hole phase.

    “Assuming Zp2β N q is also in the black hole phase, we can estimate it using bulk black hole entropies to be e ´S2 pβ N q « e ´cd Spβ N q , where Spβ N q is the thermal black hole entropy and c d is an order 1 dimension-dependent coefficient.”

  • The authors state this as an assumption.

    At least one of S(ρ_l) or S(ρ_r) is large.

    “we assume for this that at least one of Spρ l q or Spρ r q is large”

  • The paper relies on this without support.

    The fluctuations of the norm of the CFT states are suppressed, allowing normalization with the average.

    “we are using that the fluctuations of the norm of the CFT states are suppressed to normalize with the average”
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Metadata

Authors
Antonini, S., Rath, P., Sasieta, M., Swingle, B., & Vilar López, A.
Affiliations
  • University of California System (US)
  • Brandeis University (US)
  • University of British Columbia
Corresponding author
Antonini, Stefano
ORCID
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2025-12-22
Volume
2025
Issue
12
ISSN
1029-8479 (ISSN-L)
DOI
10.1007/jhep12(2025)159
OpenAlex
W7117112422
Semantic Scholar
600018c3193fe88c5dacb4edea5506423438bc72
Cited by
35
References
145
Citations by year
2026: 31 · 2025: 4
FWCI
8.81
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of High Energy Physics (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
Funders
  • U.S.~Department of Energy (DE-FOA-0002563)
  • U.S.~Department of Energy, Office of Science, Office of High Energy Physics (DE-SC0025293)
  • Heising-Simons Foundation (2024-4849)
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
Keywords
closed universe, baby universes, AdS/CFT correspondence, holography, arrow of time, effective field theory

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Antonini, S., Rath, P., Sasieta, M., Swingle, B., & Vilar López, A. (2025). The baby universe is fine and the CFT knows it: on holography for closed universes. Journal of High Energy Physics. https://doi.org/10.1007/jhep12(2025)159