Completing the holographic realization of braneworld cosmology with end-of-the-world branes: realistic expansion, gravity localization beyond the adiabatic approximation, CFT observables behind the horizon, stable top-down realizations, and quantum simulation

Antonini and Swingle (Nature Physics 16, 881–886, 2020) realized a closed FLRW braneworld cosmology inside a near-extremal charged anti-de Sitter–Reissner–Nordström black hole as a fixed-charge boundary state of a holographic conformal field theory, and showed, in an adiabatic approximation that treats the moving brane as static on the perturbation timescale, that gravity on the brane is locally localized through a metastable graviton resonance. The Discussion of that paper explicitly poses the completion of this program as open on five linked fronts: extension to cosmologies containing an accelerating (de Sitter-like) phase compatible with observational data, with gravity localization on larger spatial and temporal scales; gravity localization beyond the adiabatic approximation, i.e. how non-adiabatic brane motion modifies the spectrum and lifetime of graviton resonances; identification of the concrete conformal-field-theory observables and reconstruction protocols that probe the physics behind the black-hole horizon and thereby read out the braneworld cosmology; identification of explicit field theories whose boundary states realize the construction (top-down realizations) together with verification of dynamical stability, including whether scalar fields condense in the near-extremal background; and concrete protocols for simulating the requisite CFT states on quantum devices.

Background

The AdS/CFT correspondence (the equivalence between quantum gravity on asymptotically anti-de Sitter spacetimes, AdS, and a conformal field theory, CFT, on its boundary) provides a fully microscopic, non-perturbative definition of quantum gravity, but only for spacetimes with a timelike AdS boundary. Whether, and how, genuinely cosmological spacetimes — which have a big bang and big crunch and no such boundary — can be described within AdS/CFT is a long-standing obstacle to applying holography to our own universe.

Braneworld cosmology offers a bridge. In the Randall–Sundrum scenario, our four-dimensional world is a membrane (a brane) embedded in a five-dimensional AdS bulk; Randall and Sundrum showed that a graviton zero mode bound to a static Minkowski brane reproduces four-dimensional gravity without compactifying the extra dimension. In a bulk containing a black hole, this bound mode is lost, but Clarkson and Seahra showed that a long-lived resonant graviton mode can persist, so that gravity looks four-dimensional only below the cosmological scales on which the resonance leaks into the bulk and falls through the horizon. A useful device for such constructions is the end-of-the-world (ETW) brane: a brane that terminates the bulk spacetime, implemented holographically in Takayanagi's AdS/BCFT correspondence, where a CFT defined on a manifold with boundary is dual to AdS space truncated by a brane satisfying Neumann-type (Israel junction) boundary conditions.

Antonini and Swingle combined these ingredients. The dual CFT state is a fixed-charge boundary state evolved in imaginary time, $|\Psi\rangle=e^{-\tau_0 H}|B,Q\rangle$: a boundary state of the CFT on a sphere, prepared at fixed conserved charge $Q$, with preparation time $\tau_0>0$. Its bulk dual is a microstate of a near-extremal charged AdS–Reissner–Nordström (AdS-RN) black hole containing an ETW brane whose Euclidean trajectory starts and ends on the asymptotic boundary. After analytic continuation, the Lorentzian brane falls through the black-hole horizon and its induced metric is a closed Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology — observers on the brane experience a big bang and big crunch, while the full spacetime retains its AdS boundary and hence a CFT description. For tensor-mode gravitational perturbations, the linearized Einstein equations reduce to a one-dimensional Schrödinger equation with the brane position providing a moving boundary. Treating the brane as static (the adiabatic approximation), the authors computed the graviton resonance and showed that gravity is locally localized: four-dimensional on brane scales small compared with the cosmological ones, generalizing the Clarkson–Seahra analysis to the large charged black holes relevant here.

This was a proof of principle, and its authors explicitly list what remains open: the framework covers brane cosmologies whose expansion does not resemble ours; gravity localization was only established adiabatically; the CFT observables that encode the physics behind the black-hole horizon (and hence the cosmology) were not identified concretely; no explicit field theory with the required boundary states was constructed, nor was stability of the near-extremal background (for example against scalar condensation of the kind familiar from holographic superconductor instabilities of charged AdS black holes) verified; and the possibility of simulating such CFT states on quantum devices remained programmatic. Later work by the same and other groups has built directly on the construction.

Problem Statement

The problem is to complete the holographic (AdS/CFT) realization of braneworld cosmology initiated by Antonini and Swingle, upgrading their proof-of-principle — a closed FLRW cosmology on an end-of-the-world brane inside a near-extremal charged AdS black hole, dual to a fixed-charge boundary state $|\Psi\rangle=e^{-\tau_0 H}|B,Q\rangle$ of a holographic CFT, with gravity locally localized only in an adiabatic approximation — into a complete microscopic description of a realistic cosmology. All five requested results serve this single objective and are scientifically linked as gaps in the same construction. Completion requires a result on each of the five fronts below; the fronts are independently open, so an answer to a proper subset does not resolve the task.

1. Extend the framework to other cosmological models, in particular construct holographic braneworld cosmologies containing a de Sitter (accelerating) phase or another expansion history that could match observational cosmology, and determine whether gravity localization on the brane can be achieved on spatial and temporal scales substantially larger than those of the original construction.
2. Establish gravity localization beyond the adiabatic approximation: analyze tensor perturbations without assuming the brane is effectively static on the perturbation timescale — a moving-boundary problem for the graviton Schrödinger equation — and determine how non-adiabatic brane motion modifies the spectrum and lifetime of the graviton resonances, including whether four-dimensional gravity on the brane survives.
3. Identify the concrete CFT observables and reconstruction protocols that probe the physics behind the black-hole horizon and thereby read out the braneworld cosmology.
4. Identify explicit field theories and boundary-state constructions (top-down realizations) that furnish the required fixed-charge boundary states, and verify the dynamical stability of the bulk solutions in the complete theory, including whether scalar or other fields condense in the near-extremal black-hole background and whether the desired properties persist if they do.
5. Develop concrete proposals for simulating the requisite CFT states on quantum devices, so that the holographic braneworld cosmology can be probed experimentally.

References

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