Pith. sign in

REVIEW 4 major objections 5 minor 36 references

Matrix Multiverses Meet Multiple Mythologies

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A horizon volume of any asymptotically de Sitter space can be embedded inside a McVittie black hole in a flat $p=\rho$ FRW universe, making each such universe a finite-entropy subsystem of a larger system.

desk verdict Speculative multiverse construction with a real junction-calculation kernel, but the DEC proof is missing in the very regime the argument needs. read the letter →

arxiv 2608.08972 v2 pith:GTVQU6U6 submitted 2026-08-10 hep-th gr-qchep-ph

Sidan A , Tom Banks , Willy Fischler This is my paper · ORCID
classification hep-thgr-qchep-ph
keywords deSitterspaceMcVittieblackholeIsraeljunctionconditionsp=ρFRWuniversecovariantentropyboundfiniteHilbertrecurrencetimesmultiverse
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that a 'closed' asymptotically de Sitter universe is not a self-contained single-state system: any horizon volume of such a universe can be matched, through Israel junction conditions, to the interior of a McVittie black hole inside a flat universe filled with a maximally stiff $p=\rho$ fluid. If this embedding works, each de Sitter universe has a large number of quantum states and decays into the larger black hole system on a time scale of order $\alpha_n R_n \ln(R_n/\delta_n)$, exponentially shorter than any recurrence time. The paper argues further that no detector inside the de Sitter universe can tell whether it lives in such an embedding, so recurrence and single-state conjectures cannot be justified by observation. A sympathetic reader cares because this gives a mathematically controlled arena in which the cosmological constant and cosmological initial conditions could be environmentally selected without invoking speculative eternal inflation.

What carries the argument

The load-bearing machinery is the McVittie metric, a solution of Einstein's equations describing a Schwarzschild black hole embedded in a flat Friedmann-Robertson-Walker cosmology, together with the Israel junction conditions that paste a static de Sitter patch inside the black hole along a thin time-like shell. The shell's surface energy density $\kappa$ and pressure $p$ are computed from the discontinuity of extrinsic curvature; the critical radius $r_c=(R_s R_n^2)^{1/3}$ separates shells that expand from shells that collapse. The assertion that $\kappa \ge |p|$ (the dominant energy condition, meaning energy density dominates pressure and tension) is what allows the matching to describe a physical matter shell rather than an exotic one. A secondary mechanism is the finite fermionic matrix model whose modular Hamiltonian produces the $p=\rho$ background and the de Sitter asymptotes.

What would settle it

Evolve the thin shell in the full time-dependent McVittie metric, including the $dT\,dx$ term in Eq. (7), and compute $\kappa$ and $p$ at the shell; if $\kappa \ge |p|$ fails anywhere for initial $\delta_n>0$ and $R_s \ge R_n$, or if the shell radius cannot remain inside the black hole while staying outside the de Sitter horizon, the embedding does not describe a physical de Sitter universe inside a black hole. A simpler numerical check is to integrate the Israel equation for $\dot r^2$ from Eq. (12) with the full metric functions and see whether a turning point exists for all $R_s > R_n$.

Watch

Extended reading notes

Core claim

The paper's central claim is an extension of its earlier finite matrix-model cosmology: the flat $p=\rho$ FRW spacetime, which saturates the covariant entropy bound, can host McVittie black holes whose interiors contain entire horizon volumes of asymptotically de Sitter universes. The matching is done along a time-like shell satisfying the Israel junction conditions, with a de Sitter metric outside the shell and a Schwarzschild metric inside; the shell stress tensor is asserted to satisfy the dominant energy condition, and null rays just outside the shell do not reach the black hole horizon. Consequently an asymptotically de Sitter universe is a low-entropy subsystem of a larger, maximal-entropy system, unstable to equilibration on a detector-time scale $\alpha_n R_n \ln(R_n/\delta_n)$; the recurrence and one-dimensional-Hilbert-space pictures of a 'closed' universe are replaced by a finite-entropy subsystem that eventually thermalizes.

Load-bearing premise

The junction calculation assumes the black hole interior and the outside space can be treated as static Schwarzschild and static de Sitter even though the actual background is the time-dependent McVittie metric, and it asserts, without a displayed proof, that the shell's surface stress obeys the dominant energy condition.

Editorial extensions

If this is right

  • A closed, asymptotically de Sitter universe has a Hilbert space with many states, not a single state, because it is a finite-entropy subsystem of a larger black-hole system.
  • Recurrences never occur in this picture; the embedded de Sitter universe equilibrates with its black-hole host before any recurrence time is reached.
  • No measurement made inside the embedded universe can reveal the embedding or predict the collapse until signals from the shell arrive, so the interior is observationally indistinguishable from a genuine asymptotically de Sitter cosmology.
  • Multiple embedded universes can collide and merge on time scales set by their initial conditions in the embedding space, with catastrophic, unpredictable consequences for interior observers.
  • If the picture holds, the value of the cosmological constant and the choice of cosmological initial conditions are not fixed by fundamental dynamics alone but can be environmentally selected by the requirement that intelligent observers exist.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the junction calculation can be extended to the full time-dependent McVittie metric, the same construction would also apply to black holes whose Schwarzschild radius is comparable to the particle horizon, widening the multiverse population beyond the small-radius limit treated here.
  • The model implies that any apparently de Sitter phase in our past light cone could be a transient interior state of a larger system; the only in-principle signature would be a sudden loss of accessible causal-diamond area, which the paper argues no robust detector could survive to see.
  • A numerical evolution of the shell radius in the full McVittie background, checking the dominant energy condition and the area-matching condition for all initial shell-to-horizon distances $\delta_n$, would convert the asserted embedding from a static approximation into a tested dynamical claim.
  • Used together with a scenario in which primordial black holes seed galaxies, the same junction construction suggests that the observed dark matter could itself be a population of small embedded de Sitter universes that decayed into particles.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a model in which asymptotically de Sitter universes with cosmological radii R_n are embedded as finite-entropy subsystems inside McVittie black holes in a flat p=rho FRW background. The embedding is constructed by Israel thin-shell junction conditions along a timelike surface separating a Schwarzschild interior from an asymptotically dS exterior. The authors argue that such embedded dS universes have many quantum states, decay on timescales of order alpha_n R_n ln(R_n/delta_n), and never exhibit recurrences, and that no interior observer can tell whether she lives in such an embedded universe. The paper frames these conclusions against claims that closed dS universes have one-dimensional Hilbert spaces and that Boltzmann brain recurrences are relevant, and it sketches implications for environmental selection of the cosmological constant.

Significance. If the geometric embedding were established, the paper would make a useful contribution to the debate about the quantum description of asymptotically dS space: it gives a concrete construction in which a 'closed' dS universe is a finite-entropy subsystem of a larger system, rather than a one-dimensional Hilbert space. The authors are candid about the conjectural nature of the matrix model, the generalized Carlip-Solodukhin ansatz, and the absence of observable signatures. The use of standard Israel junction conditions is a strength, as is the explicit finite quantum-mechanical framework. However, the central embedding claim is not proven as written: the junction calculation is performed on a branch (f>0) that does not cover the regime R_s >= R_n used for the main conclusion, the dominant energy condition is asserted rather than proven, and the decay timescale is inferred rather than derived from the shell dynamics. These are load-bearing gaps, but they are in principle fixable within the manuscript's scope.

major comments (4)
  1. [Appendix A, Eqs. (17)-(20)] The junction calculation is performed only on the branch f>0. The normalization relation \dot t = sqrt(\dot r^2+f)/f in Eq. (17) and the extrinsic curvature signs in Eq. (18) assume f>0. For the embedding used in the main conclusion, the shell must satisfy R_n <= r < R_s, so the Schwarzschild-side metric has f_- = 1 - R_s/r < 0 and, if the shell encloses the dS horizon, the dS-side metric also has f_+ = 1 - r^2/R_n^2 < 0. In this branch t becomes a spatial coordinate, the sign of \dot t and the orientation of the unit normal must be re-derived, and Eqs. (19)-(20) and the inequality kappa >= |p| must be recomputed. The paper's assertion after Eq. (14) that the dominant energy condition holds is exactly the statement that the calculation is supposed to prove. Since the DEC for R_s >= R_n is a stated precondition for the physical embedding, the central claim is not established as written.
  2. [§3, Eqs. (5)-(7) and p. 6] The decay timescale is not derived from the shell equations. The paper approximates the McVittie black hole as static Schwarzschild in Minkowski space despite noting in Eq. (7) that the dT dx cross term makes the shell collapse; no bound is given on the errors introduced by setting H=0 over the interval R_n ln(R_n/delta_n). The stated lifetime alpha_n R_n ln(R_n/delta_n) is inferred from light-travel and redshift considerations, and the constants alpha_n are never defined or constrained. The statement that 'at a time of order R_s the detector hits the black hole singularity' is also asserted without calculation. Because the no-recurrence conclusion depends on this timescale, the claim is not supported.
  3. [§2, §3 and Abstract] The paper states that the embedded dS universes 'clearly have many quantum states' and that recurrences never occur. As written, these are not consequences of the Israel junction calculation; they follow only if one accepts the matrix model of [6], the generalized Carlip-Solodukhin ansatz [13-15], and the prior conjectures [7-9]. No map is given between a solution of the shell equations and the dimension or Hilbert-space structure of the corresponding quantum subsystem. If the paper's goal is a model-independent statement about closed dS universes, this step needs to be made explicit; otherwise the quantum conclusions should be attributed to the conjectural framework.
  4. [§3, Eqs. (12)-(13)] The paper claims that 'a horizon volume of any asymptotically dS space can be embedded' for R_s >= R_n, but no existence analysis is given for the shell trajectories. Eq. (12) is a first-integral-type equation with critical radius r_c = (R_s R_n^2)^{1/3}; it is not shown which initial data lead to solutions with a shell that starts near the dS horizon, satisfies the DEC, and remains on the allowed branch long enough to describe the asserted decay. The brief discussion of r > r_c and r < r_c does not cover the parameter and branch restrictions required by the main claim. An existence proof, or at least a phase-portrait analysis, is needed.
minor comments (5)
  1. [Abstract vs. body] The constants alpha_n and delta_n are introduced in the abstract, but alpha_n is never defined anywhere in the main text; the body only refers to times 'of order R_n ln(R_n/delta_n)' without the constant. Please define alpha_n or remove it from the abstract.
  2. [Eqs. (19)-(20)] Please specify which side of the shell is the 'outside' and which is the 'inside,' and state the unit normal orientation used for the extrinsic curvature; the current signs cannot be checked by the reader.
  3. [Eqs. (5)-(9)] The parameters M and R_s are introduced without an explicit relation; please state the relation used in the paper, such as R_s = 2GM or R_s = M in the chosen units, so that the McVittie-to-Schwarzschild limit in Eq. (7) can be checked.
  4. [Throughout] There are several typos and formatting issues: 'By it is very nature' at the end of §4, 'QuantuMechanics and CosMology' in ref. [7], an unbalanced bracket in Eq. (12), and '15−20' should be '15–20'. Also, the reference cited for the 'pioneering work of Israel' in §5 appears to be [35], while the Israel junction paper is [28]; please check the intended citation.
  5. [§3, final paragraph] The assertion that it is impossible for an interior detector to determine whether it is part of such a structure is stronger than the preceding statements about particular invisible parameters (R_s, collision times). Please state precisely which class of measurements the argument excludes.

Circularity Check

1 steps flagged · score 4.0 of 10

The Israel junction matching is an independent GR input, but the advertised multiverse conclusions (many quantum states, no recurrences, decay on alpha R ln(R/delta) timescales) rest on the authors' own conjectures and model choices rather than on derived predictions.

  1. self citation load bearing [Section 2, first paragraph]
    "Two of the current authors [7–9] postulated that this implied a finite dimensional Hilbert space with the Gibbons-Hawking entropy equal to the logarithm of the dimension. A more correct conjecture for the density matrix follows from the work of Carlip [13] and Solodukhin [14]. The generalization of their ansatz to dS space appeared in [15] and is supported by [10]."

    The abstract's assertion that the embedded dS universes 'clearly have many quantum states' is not derived in this paper. It is the finite-dimensional Hilbert space conjecture of refs. [7–9], generalized to a Carlip–Solodukhin density matrix in [15], with 'recent evidence' taken from [10]. All of these references are by the same author group and are explicitly conjectural; no external, machine-checked, or independently falsifiable derivation is supplied. The paper's central physical premise therefore reduces to a self-citation chain rather than to the GR junction calculation.

full rationale

The Israel junction construction (Eqs. 8–14 and Appendix A) is an independent general-relativity calculation, so the embedding claim itself is not circular. The circularity lies in the interpretive payload. The paper's assertion that the embedded dS spaces 'clearly have many quantum states' is taken from the finite-dimensional Hilbert space conjecture of refs. [7–9], modified by the generalized Carlip–Solodukhin ansatz of [15], with supporting evidence cited from [10]; all these are works by the same authors and are presented as conjectures, not as independently verified theorems. The no-recurrence conclusion is also built into the model through the time-dependent modular Hamiltonian (Eq. 3); the paragraph beginning 'Nothing prevents us...' states that the system has 'no recurrences, because the density matrix is still fluctuating randomly.' Thus the advertised consequences are either imported by self-citation or true by construction, while the actual matching calculation retains independent content. Separately, I note a missing-support issue that is not circularity: the DEC claim after Eq. (14) is asserted without proof ('It is straightforward but tedious to verify that κ≥|p|'), and the Appendix's Eq. (17) uses the f>0 branch of \dot{t}, while the R_s>R regime that the main conclusion needs has f_S<0 on the shell. This should be addressed, but it does not change the circularity score.

Assumptions & free parameters 6 free parameters · 7 assumptions · 2 invented entities

The central claim rests on a standard GR junction-condition calculation, but the multiverse interpretation and the decay timescale depend on several free parameters and on the authors' own prior conjectures about dS quantum mechanics. The p=ρ background and the finite-dimensional dS Hilbert space are taken as axioms rather than derived.

free parameters (6)
  • N* = unspecified, 'many multiples of 10^123'
    Central scale of the matrix model; controls the number of fermion fields and Hilbert space dimension. Not determined by data.
  • g = unspecified
    Coupling constant in the modular Hamiltonian (Eq. 1); affects the dynamics but is not fixed.
  • α_n = model-dependent, unspecified
    Dimensionless constants in the decay timescale α_n R_n ln(R_n/δ_n); directly control the claimed lifetime.
  • δ_n = initial conditions, unspecified
    Initial distances between the shell and the dS horizon; sets the logarithmic factor in the lifetime.
  • R_n = arbitrary for each pocket universe
    dS radii (cosmological constants) of the embedded universes; varied to represent the multiverse.
  • R_s = must be ≥ R_n, otherwise arbitrary
    Schwarzschild radius of the McVittie black hole; sets the embedding scale and final equilibration time.
assumptions (7)
  • standard math Israel junction conditions and thin-shell formalism accurately describe the interface between the dS interior and Schwarzschild exterior.
    Used in Section 3 and Appendix A to match the two metrics along a time-like shell.
  • domain assumption The covariant entropy bound (Bousso bound) is a fundamental principle.
    Used to argue that the p=ρ FRW saturates the bound and that dS space has finite entropy (Section 3).
  • domain assumption The generalized Carlip-Solodukhin ansatz describes the density matrix of dS space, implying a finite-dimensional Hilbert space with many states.
    Assumed in the Abstract and Section 2; sourced to the authors' prior conjectures [7-9,15].
  • domain assumption The p=ρ universe has an infinite-dimensional Hilbert space.
    Stated in Section 3: 'it seems clear from any point of view that it must possess an infinite dimensional Hilbert space.'
  • domain assumption ER=EPR correspondence holds: the space-like shell crossing the Einstein-Rosen bridge represents entanglement between the dS subsystem and the black hole.
    Used in Section 3 to interpret the Frolov-Mukhanov space-like branch.
  • ad hoc to paper Non-isometric encoding and the Quantum Principle of Relativity ensure unitary evolution across overlapping causal diamonds.
    Postulated in Section 1 (paragraph 3) to make time evolution and unitarity consistent; no independent evidence provided.
  • domain assumption The dS static-patch Killing vector does not generate a true time-independent Hamiltonian because there is no asymptotic boundary.
    Used in Section 2 to argue that recurrences never occur; follows from the treatment of diffeomorphisms as gauge.
invented entities (2)
  • The multiverse of asymptotically dS universes embedded in McVittie black holes in a p=ρ background
    purpose: Provides a framework for environmental selection of the c.c. and shows that dS universes have many quantum states and no recurrences.
    No interior observation can detect the embedding or other universes; the paper states detection is impossible (Section 3).
  • Fermion matrix 'blocks' representing different dS universes
    purpose: Microscopic realization of the multiverse in the matrix model.
    The block structure is postulated in Section 1 (paragraph 3) and is not observable from within any single universe.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Matrix Multiverses Meet Multiple Mythologies." pith.science (2026). https://pith.science/paper/GTVQU6U6

@misc{pith2026260808972,
  author       = {Pith},
  title        = {Pith review of: Matrix Multiverses Meet Multiple Mythologies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GTVQU6U6}},
  note         = {Machine review of arXiv:2608.08972}
}
abstract

We present a model in which asymptotically de Sitter universes of various types, and de Sitter (dS) radii $R_n$, live in the interiors of black holes in a maximally entropic flat $p = \rho$ Friedmann-Robertson-Walker universe. These dS universes clearly have many quantum states. We argue that they decay and equilibrate with the maximal entropy universe on time scales of order $\alpha_n R_n {\rm ln} (R_n /\delta_n)$, where $\alpha_n$ are model-dependent dimensionless constants and $\delta_n$ are the initial distances between the shell, satisfying the Israel junction conditions, and the dS horizon. These are time-scales as viewed by a detector following a trajectory far from the would-be cosmological horizon. These times are all exponentially shorter than dS recurrence times, which have no meaning in this model. It is impossible for a detector inside one of the dS universes to determine whether it is actually part of such a structure. This model could be used as the basis for claiming that certain constants of nature or cosmological initial conditions were chosen to have mathematically unnatural values because other values could not lead to any form of intelligent life.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

36 extracted references · 5 canonical work pages

  1. [6]

    Microscopic quantum mechanics of the p = rho universe,

    T. Banks, W. Fischler and L. Mannelli, “Microscopic quantum mechanics of the p = rho universe,” Phys. Rev. D71, 123514 (2005) doi:10.1103/PhysRevD.71.123514 [arXiv:hep-th/0408076 [hep- th]]

    arXiv 2005

  2. [1]

    The black hole interior from non-isometric codes and complexity,

    C. Akers, N. Engelhardt, D. Harlow, G. Penington and S. Vardhan, “The black hole interior from non-isometric codes and complexity,” JHEP06, 155 (2024) doi:10.1007/JHEP06(2024)155 [arXiv:2207.06536 [hep-th]]

    arXiv 2024

  3. [2]

    Holography and cosmology,

    W. Fischler and L. Susskind, “Holography and cosmology,” [arXiv:hep-th/9806039 [hep-th]]

    arXiv

  4. [3]

    A Covariant entropy conjecture,

    R. Bousso,“A Covariant entropy conjecture,” JHEP07, 004 (1999) doi:10.1088/1126- 6708/1999/07/004 [arXiv:hep-th/9905177 [hep-th]]; 10

    arXiv 1999

  5. [4]

    Holography in general space-times,

    R. Bousso, “Holography in general space-times,” JHEP06, 028 (1999) doi:10.1088/1126- 6708/1999/06/028 [arXiv:hep-th/9906022 [hep-th]]

    arXiv 1999

  6. [5]

    The Holographic principle for general backgrounds,

    R. Bousso, “The Holographic principle for general backgrounds,” Class. Quant. Grav.17, 997- 1005 (2000) doi:10.1088/0264-9381/17/5/309 [arXiv:hep-th/9911002 [hep-th]]

    arXiv 2000

  7. [7]

    QuantuMechanics and CosMology,

    T. Banks, “QuantuMechanics and CosMology,” Talk given at the festschrift for Susskind, L. Stanford University, May 2000

    2000

  8. [9]

    Taking de sitter seriously,

    W. Fischler, “Taking de sitter seriously,” Talk given at role of scaling laws in physics and biology (Celebrating the 60th birthday of Geoffrey West), Santa Fe, 19, 2000

    work page 2000

Show all 36 references
  1. [10]

    Generalized entanglement capacity of de Sitter space,

    T. Banks and P. Draper, “Generalized entanglement capacity of de Sitter space,” Phys. Rev. D 110, no.4, 045025 (2024) doi:10.1103/PhysRevD.110.045025 [arXiv:2404.13684 [hep-th]]

    2024 arXiv

  2. [11]

    Can Primordial Black Holes Be Seeds for Early Galaxies in Models Satisfying the Covariant Entropy Bound?,

    S. A, T. Banks and W. Fischler, “Can Primordial Black Holes Be Seeds for Early Galaxies in Models Satisfying the Covariant Entropy Bound?,” [arXiv:2607.01292 [hep-ph]]

    arXiv

  3. [12]

    Cosmological Event Horizons, Thermodynamics, and Par- ticle Creation,

    G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Par- ticle Creation,” Phys. Rev. D15, 2738-2751 (1977) doi:10.1103/PhysRevD.15.2738

    1977 doi

  4. [13]

    Black hole entropy from conformal field theory in any dimension,

    S. Carlip, “Black hole entropy from conformal field theory in any dimension,” Phys. Rev. Lett. 82, 2828-2831 (1999) doi:10.1103/PhysRevLett.82.2828 [arXiv:hep-th/9812013 [hep-th]]

    1999 arXiv

  5. [14]

    Conformal description of horizon’s states,

    S. N. Solodukhin, “Conformal description of horizon’s states,” Phys. Lett. B454, 213-222 (1999) doi:10.1016/S0370-2693(99)00398-6 [arXiv:hep-th/9812056 [hep-th]]

    1999 arXiv

  6. [15]

    Conformal description of near-horizon vacuum states,

    T. Banks and K. M. Zurek, “Conformal description of near-horizon vacuum states,” Phys. Rev. D104, no.12, 126026 (2021) doi:10.1103/PhysRevD.104.126026 [arXiv:2108.04806 [hep-th]]

    2021 arXiv

  7. [16]

    Bayes Keeps Boltzmann Brains at Bay,

    D. N. Page, in Universe or Multiverse?, edited by B. J. Carr (Cambridge Uni- versity Press, Cam- bridge, 2007), pp. 401-419; hep-th/0610101; For a list of more recent references see D. N. Page, “Bayes Keeps Boltzmann Brains at Bay,” Found. Phys.54, no.5, 62 (2024) doi:10.1007/...

    2024 arXiv

  8. [17]

    Recurrent nightmares? Measurement theory in de Sitter space,

    T. Banks, W. Fischler and S. Paban,“Recurrent nightmares? Measurement theory in de Sitter space,” JHEP12, 062 (2002) doi:10.1088/1126-6708/2002/12/062 [arXiv:hep-th/0210160 [hep- th]]

    2002 arXiv

  9. [18]

    Effective field theory, black holes, and the cos- mological constant,

    A. G. Cohen, D. B. Kaplan and A. E. Nelson, “Effective field theory, black holes, and the cos- mological constant,” Phys. Rev. Lett.82, 4971-4974 (1999) doi:10.1103/PhysRevLett.82.4971 [arXiv:hep-th/9803132 [hep-th]]

    1999 arXiv

  10. [19]

    Remarks on the Cohen-Kaplan-Nelson bound,

    T. Banks and P. Draper, “Remarks on the Cohen-Kaplan-Nelson bound,” Phys. Rev. D101, no.12, 126010 (2020) doi:10.1103/PhysRevD.101.126010 [arXiv:1911.05778 [hep-th]]

    2020 arXiv

  11. [20]

    Densities of states and the Cohen-Kaplan-Nelson bound,

    N. Blinov and P. Draper, “Densities of states and the Cohen-Kaplan-Nelson bound,” Phys. Rev. D104, no.7, 076024 (2021) doi:10.1103/PhysRevD.104.076024 [arXiv:2107.03530 [hep-ph]]; 11

    2021 arXiv

  12. [21]

    Gravitational contributions to the electrong-factor,

    A. G. Cohen and D. B. Kaplan, “Gravitational contributions to the electrong-factor,” [arXiv:2103.04509 [hep-ph]]

    arXiv

  13. [22]

    Fast Scramblers,

    Y. Sekino and L. Susskind, “Fast Scramblers,” JHEP10, 065 (2008) doi:10.1088/1126- 6708/2008/10/065 [arXiv:0808.2096 [hep-th]]

    2008 arXiv

  14. [23]

    Quantum mechanics and observers for gravity in a closed universe,

    D. Harlow, M. Usatyuk and Y. Zhao, “Quantum mechanics and observers for gravity in a closed universe,” JHEP02, 108 (2026) doi:10.1007/JHEP02(2026)108 [arXiv:2501.02359 [hep-th]]

    2026 arXiv

  15. [24]

    ”It from Bit

    Y. Zhao,“”It from Bit”: The Hartle-Hawking state and quantum mechanics for de Sitter ob- servers,” [arXiv:2602.05939 [hep-th]]

  16. [25]

    The gravitational path integral from an observer’s point of view,

    A. I. Abdalla, S. Antonini, L. V. Iliesiu and A. Levine, “The gravitational path integral from an observer’s point of view,” JHEP05, 059 (2025) doi:10.1007/JHEP05(2025)059 [arXiv:2501.02632 [hep-th]]

    2025 arXiv

  17. [26]

    Transcending the ensemble: baby universes, spacetime worm- holes, and the order and disorder of black hole information,

    D. Marolf and H. Maxfield, “Transcending the ensemble: baby universes, spacetime worm- holes, and the order and disorder of black hole information,” JHEP08, 044 (2020) doi:10.1007/JHEP08(2020)044 [arXiv:2002.08950 [hep-th]]

    2020 arXiv

  18. [27]

    The holographic approach to cosmology,

    T. Banks and W. Fischler,“The holographic approach to cosmology,” [arXiv:hep-th/0412097 [hep- th]]

    arXiv

  19. [28]

    Singular hypersurfaces and thin shells in general relativity,

    W. Israel,“Singular hypersurfaces and thin shells in general relativity,” Nuovo Cim. B44S10 (1966), 1 [erratum: Nuovo Cim. B48(1967), 463] doi:10.1007/BF02710419

    1966 doi

  20. [29]

    THROUGH A BLACK HOLE INTO A NEW UNIVERSE?,

    V. P. Frolov, M. A. Markov and V. F. Mukhanov, “THROUGH A BLACK HOLE INTO A NEW UNIVERSE?,” Phys. Lett. B216, 272-276 (1989) doi:10.1016/0370-2693(89)91114-3

    1989 doi

  21. [30]

    Black Holes as Possible Sources of Closed and Semiclosed Worlds,

    V. P. Frolov, M. A. Markov and V. F. Mukhanov, “Black Holes as Possible Sources of Closed and Semiclosed Worlds,” Phys. Rev. D41, 383 (1990) doi:10.1103/PhysRevD.41.383

    1990 doi

  22. [31]

    Cool horizons for entangled black holes,

    J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” Fortsch. Phys.61, 781-811 (2013) doi:10.1002/prop.201300020 [arXiv:1306.0533 [hep-th]]

    2013 arXiv

  23. [32]

    Holographic spacetime model of inflation and its predictions for the CMB primordial spectra,

    S. A and T. Banks, “Holographic spacetime model of inflation and its predictions for the CMB primordial spectra,” Phys. Rev. D112, no.2, 023516 (2025) doi:10.1103/xts8-ggmg [arXiv:2502.15108 [hep-th]]

    2025 arXiv

  24. [33]

    Anthropic Bound on the Cosmological Constant,

    S. Weinberg, “Anthropic Bound on the Cosmological Constant,” Phys. Rev. Lett.59, 2607 (1987) doi:10.1103/PhysRevLett.59.2607

    1987 doi

  25. [34]

    Cosmological breaking of supersymmetry?,

    T. Banks, “Cosmological breaking of supersymmetry?,” Int. J. Mod. Phys. A16, 910-921 (2001) doi:10.1142/S0217751X01003998 [arXiv:hep-th/0007146 [hep-th]]; T. Banks, “Old Ideas for New Physicists 2,” [arXiv:2307.15812 [hep-ph]]

    2001 arXiv

  26. [35]

    Thermo field dynamics of black holes,

    W. Israel,“Thermo field dynamics of black holes,” Phys. Lett. A57(1976), 107-110 doi:10.1016/0375-9601(76)90178-X

    1976 doi

  27. [36]

    Eternal black holes in anti-de Sitter,

    J. M. Maldacena, “Eternal black holes in anti-de Sitter,” JHEP04, 021 (2003) doi:10.1088/1126- 6708/2003/04/021 [arXiv:hep-th/0106112 [hep-th]]

    2003 arXiv

  28. [37]

    Thermodynamics of space-time: The Einstein equation of state,

    T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state,” Phys. Rev. Lett. 75(1995), 1260-1263 doi:10.1103/PhysRevLett.75.1260 [arXiv:gr-qc/9504004 [gr-qc]]. 12

    1995 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.