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Strong-coupling dynamics and entanglement in de Sitter space
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 18 March 2021

Strong-coupling dynamics and entanglement in de Sitter space

  • Jorge Casalderrey-Solana1,
  • Christian Ecker  ORCID: orcid.org/0000-0002-8669-43002,
  • David Mateos1,3 &
  • …
  • Wilke van der Schee4 

Journal of High Energy Physics volume 2021, Article number: 181 (2021) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

We use holography to study the dynamics of a strongly-coupled gauge theory in four-dimensional de Sitter space with Hubble rate H. The gauge theory is non-conformal with a characteristic mass scale M. We solve Einstein’s equations numerically and determine the time evolution of homogeneous gauge theory states. If their initial energy density is high compared with H4 then the early-time evolution is well described by viscous hydrodynamics with a non-zero bulk viscosity. At late times the dynamics is always far from equilibrium. The asymptotic late-time state preserves the full de Sitter symmetry group and its dual geometry is a domain-wall in AdS5. The approach to this state is characterised by an emergent relation of the form \( \mathcal{P} \) = w ℰ that is different from the equilibrium equation of state in flat space. The constant w does not depend on the initial conditions but only on H/M and is negative if the ratio H/M is close to unity. The event and the apparent horizons of the late-time solution do not coincide with one another, reflecting its non-equilibrium nature. In between them lies an “entanglement horizon” that cannot be penetrated by extremal surfaces anchored at the boundary, which we use to compute the entanglement entropy of boundary regions. If the entangling region equals the observable universe then the extremal surface coincides with a bulk cosmological horizon that just touches the event horizon, while for larger regions the extremal surface probes behind the event horizon.

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Authors and Affiliations

  1. Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICC), Universitat de Barcelona, Martí i Franquès 1, ES-08028, Barcelona, Spain

    Jorge Casalderrey-Solana & David Mateos

  2. Institut für Theoretische Physik, Goethe Universität, Max-von-Laue-Str. 1, 60438, Frankfurt am Main, Germany

    Christian Ecker

  3. Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, ES-08010, Barcelona, Spain

    David Mateos

  4. Theoretical Physics Department, CERN, CH-1211, Genève 23, Switzerland

    Wilke van der Schee

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  1. Jorge Casalderrey-Solana
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  2. Christian Ecker
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  4. Wilke van der Schee
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Correspondence to Wilke van der Schee.

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Casalderrey-Solana, J., Ecker, C., Mateos, D. et al. Strong-coupling dynamics and entanglement in de Sitter space. J. High Energ. Phys. 2021, 181 (2021). https://doi.org/10.1007/JHEP03(2021)181

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  • Received: 26 November 2020

  • Accepted: 04 February 2021

  • Published: 18 March 2021

  • DOI: https://doi.org/10.1007/JHEP03(2021)181

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Keywords

  • Gauge-gravity correspondence
  • AdS-CFT Correspondence
  • Nonperturbative Effects
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