Skip to content
DraconiticResearch
Search Sources API
203,952 studies31 sourcesUpdated 4 min ago
PreprintCC BY 4.0Zenodo

Non-Equilibrium Holographic Brane Cosmology in AdS5. I-A: Operator Algebras in the Static Patch, Type II_1 Reduction, and Holographic Reconstruction

  • Alan Conrad Carrasco1
  1. 1Independent Researcher
Open at sourcePDFDOICite

Abstract

The local description of cosmological horizons in quantum gravity faces a fundamental algebraic obstruction: in the static patch of four-dimensional de Sitter space (dS4), the algebra of local quantum observables forms a hyperfinite Type III1 von Neumann factor, precluding an invariant vacuum state, a well-defined density matrix, and a normalizable trace.

In this work, the first of a dedicated series developing non-equilibrium holographic cosmology on Karch-Randall 3-branes embedded in asymptotically AdS5 spacetimes, we provide an analytical framework addressing cosmological horizon unitarity. By coupling the local quantum fields to the dynamical Hamiltonian of a timelike observer via a crossed product construction, we lift the algebra to a Type II∞ factor. Incorporating the non-perturbative Nariai black hole collapse limit provides a natural energy regularization that projects the extended algebra onto a finite, hyperfinite Type II1 von Neumann factor AdS equipped with a unique, faithful, normalized trace τ.

We construct the physical Hilbert space HdS via the Gelfand-Naimark-Segal (GNS) representation and show that the maximum algebraic entropy rigorously saturates the Gibbons-Hawking area bound. Finally, we formulate the quantum isometric embedding V: HdS → Hphys into the asymptotic conformal boundary I+, establish the holographic dictionary via the canonical Petz recovery channel, and prove that the proper time of the comoving observer emerges directly as the canonical conjugate variable to the asymptotic entanglement modular flow through Jafferis-Lewkowycz-Maldacena-Suh (JLMS) duality.

Related

  1. Non-Equilibrium Holographic Brane Cosmology in AdS5. I-B: 5D Stellar Collapse, Modified Shiromizu-Maeda-Sasaki Bounce Dynamics, and Primordial CMB Signatures
    Alan Conrad Carrasco
    ZenodoPreprintCC BY 4.0Full textZenodo
  2. Non-Equilibrium Holographic Brane Cosmology in AdS5. I-C: Graviton Spectral Decomposition, Higuchi Ghost Protection, and Non-Linear Vainshtein Screening on the Karch-Randall Brane
    Alan Conrad Carrasco
    ZenodoPreprintCC BY 4.0Full textZenodo
  3. Non-Equilibrium Holographic Brane Cosmology in AdS5. I-D: Stochastic Moduli Freeze-Out, Non-Supersymmetric Standard Model Vacuum Cancellation, and Radion Stabilization
    Alan Conrad Carrasco
    ZenodoPreprintCC BY 4.0Full textZenodo
  4. Non-Equilibrium Holographic Brane Cosmology in AdS5. II: Bulk Angular Momentum, Bianchi Type IX Regular Bounce, and CMB Parity-Odd Imprints
    Alan Conrad Carrasco
    ZenodoPreprintCC BY 4.0Full textZenodo
  5. Holographic dark energy in Einstein-Cartan spin cosmology
    Yongjun Yun, Jungjai Lee
    arXivPreprintCC BY 4.0Full textGravitation & general relativityarXiv

Cite

BibTeXRIS
BibTeX
@misc{carrasco2026nonequilibrium,
  title = {{Non-Equilibrium Holographic Brane Cosmology in AdS5. I-A: Operator Algebras in the Static Patch, Type II_1 Reduction, and Holographic Reconstruction}},
  author = {Alan Conrad Carrasco},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23490315},
  url = {https://zenodo.org/records/23490315},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Non-Equilibrium Holographic Brane Cosmology in AdS5. I-A: Operator Algebras in the Static Patch, Type II_1 Reduction, and Holographic Reconstruction
AU  - Alan Conrad Carrasco
PY  - 2026
DA  - 2026/10/20
PB  - Zenodo
DO  - 10.5281/zenodo.23490315
UR  - https://zenodo.org/records/23490315
AB  - The local description of cosmological horizons in quantum gravity faces a fundamental algebraic obstruction: in the static patch of four-dimensional de Sitter space (dS4), the algebra of local quantum observables forms a hyperfinite Type III1 von Neumann factor, precluding an invariant vacuum state, a well-defined density matrix, and a normalizable trace.  In this work, the first of a dedicated series developing non-equilibrium holographic cosmology on Karch-Randall 3-branes embedded in asymptotically AdS5 spacetimes, we provide an analytical framework addressing cosmological horizon unitarity. By coupling the local quantum fields to the dynamical Hamiltonian of a timelike observer via a crossed product construction, we lift the algebra to a Type II∞ factor. Incorporating the non-perturbative Nariai black hole collapse limit provides a natural energy regularization that projects the extended algebra onto a finite, hyperfinite Type II1 von Neumann factor AdS equipped with a unique, faithful, normalized trace τ.  We construct the physical Hilbert space HdS via the Gelfand-Naimark-Segal (GNS) representation and show that the maximum algebraic entropy rigorously saturates the Gibbons-Hawking area bound. Finally, we formulate the quantum isometric embedding V: HdS → Hphys into the asymptotic conformal boundary I+, establish the holographic dictionary via the canonical Petz recovery channel, and prove that the proper time of the comoving observer emerges directly as the canonical conjugate variable to the asymptotic entanglement modular flow through Jafferis-Lewkowycz-Maldacena-Suh (JLMS) duality.
ER  -