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Title: Cosmic equilibration: A holographic no-hair theorem from the generalized second law

Abstract

In a wide class of cosmological models, a positive cosmological constant drives cosmological evolution toward an asymptotically de Sitter phase. Here we connect this behavior to the increase of entropy over time, based on the idea that de Sitter spacetime is a maximum-entropy state. We prove a cosmic no-hair theorem for Robertson-Walker and Bianchi I spacetimes that admit a Q-screen (“quantum” holographic screen) with certain entropic properties: If generalized entropy, in the sense of the cosmological version of the generalized second law conjectured by Bousso and Engelhardt, increases up to a finite maximum value along the screen, then the spacetime is asymptotically de Sitter in the future. Moreover, the limiting value of generalized entropy coincides with the de Sitter horizon entropy. We do not use the Einstein field equations in our proof, nor do we assume the existence of a positive cosmological constant. As such, asymptotic relaxation to a de Sitter phase can, in a precise sense, be thought of as cosmological equilibration.

Authors:
;
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1422463
Alternate Identifier(s):
OSTI ID: 1501535
Grant/Contract Number:  
SC0011632
Resource Type:
Published Article
Journal Name:
Physical Review. D.
Additional Journal Information:
Journal Name: Physical Review. D. Journal Volume: 97 Journal Issue: 4; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Carroll, Sean M., and Chatwin-Davies, Aidan. Cosmic equilibration: A holographic no-hair theorem from the generalized second law. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.97.046012.
Carroll, Sean M., & Chatwin-Davies, Aidan. Cosmic equilibration: A holographic no-hair theorem from the generalized second law. United States. https://doi.org/10.1103/PhysRevD.97.046012
Carroll, Sean M., and Chatwin-Davies, Aidan. Fri . "Cosmic equilibration: A holographic no-hair theorem from the generalized second law". United States. https://doi.org/10.1103/PhysRevD.97.046012.
@article{osti_1422463,
title = {Cosmic equilibration: A holographic no-hair theorem from the generalized second law},
author = {Carroll, Sean M. and Chatwin-Davies, Aidan},
abstractNote = {In a wide class of cosmological models, a positive cosmological constant drives cosmological evolution toward an asymptotically de Sitter phase. Here we connect this behavior to the increase of entropy over time, based on the idea that de Sitter spacetime is a maximum-entropy state. We prove a cosmic no-hair theorem for Robertson-Walker and Bianchi I spacetimes that admit a Q-screen (“quantum” holographic screen) with certain entropic properties: If generalized entropy, in the sense of the cosmological version of the generalized second law conjectured by Bousso and Engelhardt, increases up to a finite maximum value along the screen, then the spacetime is asymptotically de Sitter in the future. Moreover, the limiting value of generalized entropy coincides with the de Sitter horizon entropy. We do not use the Einstein field equations in our proof, nor do we assume the existence of a positive cosmological constant. As such, asymptotic relaxation to a de Sitter phase can, in a precise sense, be thought of as cosmological equilibration.},
doi = {10.1103/PhysRevD.97.046012},
journal = {Physical Review. D.},
number = 4,
volume = 97,
place = {United States},
year = {Fri Feb 23 00:00:00 EST 2018},
month = {Fri Feb 23 00:00:00 EST 2018}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevD.97.046012

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Cited by: 19 works
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Works referenced in this record:

Genuine cosmic hair
journal, January 2017

  • Kastor, David; Ray, Sourya; Traschen, Jennie
  • Classical and Quantum Gravity, Vol. 34, Issue 4
  • DOI: 10.1088/1361-6382/aa5735

Entanglement Equilibrium and the Einstein Equation
journal, May 2016


Building up spacetime with quantum entanglement
journal, June 2010


The four laws of black hole mechanics
journal, June 1973

  • Bardeen, J. M.; Carter, B.; Hawking, S. W.
  • Communications in Mathematical Physics, Vol. 31, Issue 2
  • DOI: 10.1007/BF01645742

Building up Space–Time with Quantum Entanglement
journal, December 2010


The de Sitter spacetime as an attractor solution in fourth-order gravity
journal, January 1988


The cosmic no-hair theorem and the non-linear stability of homogeneous Newtonian cosmological models
journal, September 1994


de Sitter equilibrium as a fundamental framework for cosmology
journal, June 2009


Marginally trapped tubes and dynamical horizons
journal, December 2005


Infrared stability of de Sitter space: Loop corrections to scalar propagators
journal, November 2010


Theory of cosmological perturbations
journal, June 1992


Cosmological event horizons, thermodynamics, and particle creation
journal, May 1977


Gravitational dynamics from entanglement “thermodynamics”
journal, April 2014

  • Lashkari, Nima; McDermott, Michael B.; Van Raamsdonk, Mark
  • Journal of High Energy Physics, Vol. 2014, Issue 4
  • DOI: 10.1007/JHEP04(2014)195

What is the entropy in entropic gravity?
journal, June 2016


Black holes in general relativity
journal, June 1972

  • Hawking, S. W.
  • Communications in Mathematical Physics, Vol. 25, Issue 2
  • DOI: 10.1007/BF01877517

Dynamical horizons and their properties
journal, November 2003


Thermodynamical aspects of gravity: new insights
journal, March 2010


Holographic entanglement entropy conjecture for general spacetimes
journal, October 2016


Revisiting cosmic no-hair theorem for inflationary settings
journal, June 2012


General Relativity
book, January 1984


Generalized second law of thermodynamics in black-hole physics
journal, June 1974


Cosmic no-hair theorems and inflation
journal, March 1987


Cosmic no-hair theorem in power-law inflation
journal, February 1992


Isolated and Dynamical Horizons and Their Applications
journal, December 2004

  • Ashtekar, Abhay; Krishnan, Badri
  • Living Reviews in Relativity, Vol. 7, Issue 1
  • DOI: 10.12942/lrr-2004-10

Cosmic no-hair theorem in homogeneous spacetimes. I. Bianchi models
journal, April 1993


De Sitter Holography with a Finite Number of States
journal, January 2005


Proof of a quantum Bousso bound
journal, August 2014


Space from Hilbert space: Recovering geometry from bulk entanglement
journal, January 2017


Cosmological Breaking of Supersymmetry?
journal, February 2001


Disturbing Implications of a Cosmological Constant
journal, October 2002


Inhomogeneous anisotropic cosmology
journal, October 2016


Holographic equipartition and the maximization of entropy
journal, September 2017


New Area Law in General Relativity
journal, August 2015


The asymptotic approach to de Sitter space-time
journal, November 1989


Generalized second law for cosmology
journal, January 2016


Holography in general space-times
journal, June 1999


Black-hole boundaries
journal, November 2005

  • Booth, Ivan
  • Canadian Journal of Physics, Vol. 83, Issue 11
  • DOI: 10.1139/p05-063

Cool horizons for entangled black holes
journal, August 2013


Proof of a new area law in general relativity
journal, August 2015


Quantum focusing conjecture
journal, March 2016


On the origin of gravity and the laws of Newton
journal, April 2011


Correlators, Feynman Diagrams, and Quantum No-hair in deSitter Spacetime
journal, February 2013


Thermodynamics of Spacetime: The Einstein Equation of State
journal, August 1995


Dynamical Horizons: Energy, Angular Momentum, Fluxes, and Balance Laws
journal, December 2002


Cosmic no-hair: nonlinear asymptotic stability of de Sitter universe
journal, February 2002


Geodesic-light-cone coordinates and the Bianchi I spacetime
journal, June 2016

  • Fleury, Pierre; Nugier, Fabien; Fanizza, Giuseppe
  • Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 06
  • DOI: 10.1088/1475-7516/2016/06/008

A Local View of the Observable Universe
journal, March 1995


Infrared stability of de Sitter QFT: Results at all orders
journal, August 2011


Observations in Some Simple Cosmological Models with Shear
journal, January 1969

  • Saunders, P. T.
  • Monthly Notices of the Royal Astronomical Society, Vol. 142, Issue 2
  • DOI: 10.1093/mnras/142.2.213

Gravitation from entanglement in holographic CFTs
journal, March 2014

  • Faulkner, Thomas; Guica, Monica; Hartman, Thomas
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)051

Entanglement renormalization and holography
journal, September 2012


General laws of black-hole dynamics
journal, June 1994


Can the universe afford inflation?
journal, September 2004