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}
}
https://doi.org/10.1103/PhysRevD.97.046012
Web of Science
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
Entanglement Equilibrium and the Einstein Equation
journal, May 2016
- Jacobson, Ted
- Physical Review Letters, Vol. 116, Issue 20
Building up spacetime with quantum entanglement
journal, June 2010
- Van Raamsdonk, Mark
- General Relativity and Gravitation, Vol. 42, Issue 10
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
Building up Space–Time with Quantum Entanglement
journal, December 2010
- Van Raamsdonk, Mark
- International Journal of Modern Physics D, Vol. 19, Issue 14
The de Sitter spacetime as an attractor solution in fourth-order gravity
journal, January 1988
- Schmidt, H. -J
- Classical and Quantum Gravity, Vol. 5, Issue 1
The cosmic no-hair theorem and the non-linear stability of homogeneous Newtonian cosmological models
journal, September 1994
- Brauer, Uwe; Rendall, Alan; Reula, Oscar
- Classical and Quantum Gravity, Vol. 11, Issue 9
de Sitter equilibrium as a fundamental framework for cosmology
journal, June 2009
- Albrecht, Andreas
- Journal of Physics: Conference Series, Vol. 174
Marginally trapped tubes and dynamical horizons
journal, December 2005
- Booth, Ivan; Brits, Lionel; Gonzalez, Jose A.
- Classical and Quantum Gravity, Vol. 23, Issue 2
Infrared stability of de Sitter space: Loop corrections to scalar propagators
journal, November 2010
- Marolf, Donald; Morrison, Ian A.
- Physical Review D, Vol. 82, Issue 10
Theory of cosmological perturbations
journal, June 1992
- Mukhanov, V.
- Physics Reports, Vol. 215, Issue 5-6
Cosmological event horizons, thermodynamics, and particle creation
journal, May 1977
- Gibbons, G. W.; Hawking, S. W.
- Physical Review D, Vol. 15, Issue 10
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
What is the entropy in entropic gravity?
journal, June 2016
- Carroll, Sean M.; Remmen, Grant N.
- Physical Review D, Vol. 93, Issue 12
Black holes in general relativity
journal, June 1972
- Hawking, S. W.
- Communications in Mathematical Physics, Vol. 25, Issue 2
Dynamical horizons and their properties
journal, November 2003
- Ashtekar, Abhay; Krishnan, Badri
- Physical Review D, Vol. 68, Issue 10
Thermodynamical aspects of gravity: new insights
journal, March 2010
- Padmanabhan, T.
- Reports on Progress in Physics, Vol. 73, Issue 4
Holographic entanglement entropy conjecture for general spacetimes
journal, October 2016
- Sanches, Fabio; Weinberg, Sean J.
- Physical Review D, Vol. 94, Issue 8
Revisiting cosmic no-hair theorem for inflationary settings
journal, June 2012
- Maleknejad, A.; Sheikh-Jabbari, M. M.
- Physical Review D, Vol. 85, Issue 12
Generalized second law of thermodynamics in black-hole physics
journal, June 1974
- Bekenstein, Jacob D.
- Physical Review D, Vol. 9, Issue 12
Cosmic no-hair theorems and inflation
journal, March 1987
- Barrow, John D.
- Physics Letters B, Vol. 187, Issue 1-2
Cosmic no-hair theorem in power-law inflation
journal, February 1992
- Kitada, Yuichi; Maeda, Kei-ichi
- Physical Review D, Vol. 45, Issue 4
Isolated and Dynamical Horizons and Their Applications
journal, December 2004
- Ashtekar, Abhay; Krishnan, Badri
- Living Reviews in Relativity, Vol. 7, Issue 1
Cosmic no-hair theorem in homogeneous spacetimes. I. Bianchi models
journal, April 1993
- Kitada, Y.; Maeda, K.
- Classical and Quantum Gravity, Vol. 10, Issue 4
De Sitter Holography with a Finite Number of States
journal, January 2005
- Parikh, Maulik; Verlinde, Erik
- Journal of High Energy Physics, Vol. 2005, Issue 01
Proof of a quantum Bousso bound
journal, August 2014
- Bousso, Raphael; Casini, Horacio; Fisher, Zachary
- Physical Review D, Vol. 90, Issue 4
Space from Hilbert space: Recovering geometry from bulk entanglement
journal, January 2017
- Cao, ChunJun; Carroll, Sean M.; Michalakis, Spyridon
- Physical Review D, Vol. 95, Issue 2
Cosmological Breaking of Supersymmetry?
journal, February 2001
- Banks, T.
- International Journal of Modern Physics A, Vol. 16, Issue 05
Disturbing Implications of a Cosmological Constant
journal, October 2002
- Dyson, Lisa; Kleban, Matthew; Susskind, Leonard
- Journal of High Energy Physics, Vol. 2002, Issue 10
Inhomogeneous anisotropic cosmology
journal, October 2016
- Kleban, Matthew; Senatore, Leonardo
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 10
Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant
journal, October 1983
- Wald, Robert M.
- Physical Review D, Vol. 28, Issue 8
Holographic equipartition and the maximization of entropy
journal, September 2017
- Krishna, P. B.; Mathew, Titus K.
- Physical Review D, Vol. 96, Issue 6
New Area Law in General Relativity
journal, August 2015
- Bousso, Raphael; Engelhardt, Netta
- Physical Review Letters, Vol. 115, Issue 8
The asymptotic approach to de Sitter space-time
journal, November 1989
- Barrow, John D.; Götz, Günter
- Physics Letters B, Vol. 231, Issue 3
Generalized second law for cosmology
journal, January 2016
- Bousso, Raphael; Engelhardt, Netta
- Physical Review D, Vol. 93, Issue 2
Holography in general space-times
journal, June 1999
- Bousso, Raphael
- Journal of High Energy Physics, Vol. 1999, Issue 06
Black-hole boundaries
journal, November 2005
- Booth, Ivan
- Canadian Journal of Physics, Vol. 83, Issue 11
Cool horizons for entangled black holes
journal, August 2013
- Maldacena, J.; Susskind, L.
- Fortschritte der Physik, Vol. 61, Issue 9
Proof of a new area law in general relativity
journal, August 2015
- Bousso, Raphael; Engelhardt, Netta
- Physical Review D, Vol. 92, Issue 4
Quantum focusing conjecture
journal, March 2016
- Bousso, Raphael; Fisher, Zachary; Leichenauer, Stefan
- Physical Review D, Vol. 93, Issue 6
On the origin of gravity and the laws of Newton
journal, April 2011
- Verlinde, Erik
- Journal of High Energy Physics, Vol. 2011, Issue 4
Correlators, Feynman Diagrams, and Quantum No-hair in deSitter Spacetime
journal, February 2013
- Hollands, Stefan
- Communications in Mathematical Physics, Vol. 319, Issue 1
Thermodynamics of Spacetime: The Einstein Equation of State
journal, August 1995
- Jacobson, Ted
- Physical Review Letters, Vol. 75, Issue 7
Dynamical Horizons: Energy, Angular Momentum, Fluxes, and Balance Laws
journal, December 2002
- Ashtekar, Abhay; Krishnan, Badri
- Physical Review Letters, Vol. 89, Issue 26
Cosmic no-hair: nonlinear asymptotic stability of de Sitter universe
journal, February 2002
- Bruni, Marco; Mena, Filipe C.; Tavakol, Reza
- Classical and Quantum Gravity, Vol. 19, Issue 5
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
A Local View of the Observable Universe
journal, March 1995
- Bruni, Marco; Matarrese, Sabino; Pantano, Ornella
- Physical Review Letters, Vol. 74, Issue 11
Infrared stability of de Sitter QFT: Results at all orders
journal, August 2011
- Marolf, Donald; Morrison, Ian A.
- Physical Review D, Vol. 84, Issue 4
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
Gravitation from entanglement in holographic CFTs
journal, March 2014
- Faulkner, Thomas; Guica, Monica; Hartman, Thomas
- Journal of High Energy Physics, Vol. 2014, Issue 3
Entanglement renormalization and holography
journal, September 2012
- Swingle, Brian
- Physical Review D, Vol. 86, Issue 6
General laws of black-hole dynamics
journal, June 1994
- Hayward, Sean A.
- Physical Review D, Vol. 49, Issue 12
Can the universe afford inflation?
journal, September 2004
- Albrecht, Andreas; Sorbo, Lorenzo
- Physical Review D, Vol. 70, Issue 6