Asymptotic Behavior of Cosmologies with $$\Lambda >0$$ in $$2+1$$ Dimensions

Creminelli, Paolo; Senatore, Leonardo; Vasy, András

doi:10.1007/s00220-020-03706-3

Title: Asymptotic Behavior of Cosmologies with $$$$\Lambda >0$$$$ in $$2+1$$ Dimensions

Abstract

We study, using mean curvature flow methods, 2+1 dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler characteristic and are initially expanding everywhere, then we prove that the spatial slices reach infinite volume, asymptotically converge on average to de Sitter and they become, almost everywhere, physically indistinguishable from de Sitter. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations and the formation of black holes.

Authors:

Creminelli, Paolo ^[1]; Senatore, Leonardo ^[2];

^[3]

Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Inst. for Fundamental Physics of the Universe (IFPU), Trieste (Italy)
Stanford Univ., CA (United States). Stanford Inst. of Theoretical Physics (ITP); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Stanford Univ., CA (United States)

Publication Date:: Wed Mar 11 00:00:00 EDT 2020

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1638080

Grant/Contract Number:: AC02-76SF00515; 1664683; 1720397

Resource Type:: Accepted Manuscript

Journal Name:: Communications in Mathematical Physics

Additional Journal Information:: Journal Volume: 376; Journal Issue: 2; Journal ID: ISSN 0010-3616

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS

Citation Formats


                    Creminelli, Paolo, Senatore, Leonardo, and Vasy, András. Asymptotic Behavior of Cosmologies with $$\Lambda >0$$ in $$2+1$$ Dimensions.  United States: N. p., 2020. 
Web.  doi:10.1007/s00220-020-03706-3.

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                    Creminelli, Paolo, Senatore, Leonardo, & Vasy, András. Asymptotic Behavior of Cosmologies with $$\Lambda >0$$ in $$2+1$$ Dimensions.  United States.  https://doi.org/10.1007/s00220-020-03706-3

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                    Creminelli, Paolo, Senatore, Leonardo, and Vasy, András. Wed .  
"Asymptotic Behavior of Cosmologies with $$\Lambda >0$$ in $$2+1$$ Dimensions".  United States.  https://doi.org/10.1007/s00220-020-03706-3.  https://www.osti.gov/servlets/purl/1638080.

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@article{osti_1638080,

  title        = {Asymptotic Behavior of Cosmologies with $$\Lambda >0$$ in $$2+1$$ Dimensions},

  author       = {Creminelli, Paolo and Senatore, Leonardo and Vasy, András},

  abstractNote = {We study, using mean curvature flow methods, 2+1 dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler characteristic and are initially expanding everywhere, then we prove that the spatial slices reach infinite volume, asymptotically converge on average to de Sitter and they become, almost everywhere, physically indistinguishable from de Sitter. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations and the formation of black holes.},

  doi          = {10.1007/s00220-020-03706-3},

  journal      = {Communications in Mathematical Physics},

  number       = 2,

  volume       = 376,

  place        = {United States},

  year         = {Wed Mar 11 00:00:00 EDT 2020},

  month        = {Wed Mar 11 00:00:00 EDT 2020}

}

Copy to clipboard

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Works referenced in this record:

Robustness of inflation to inhomogeneous initial conditions
journal, September 2017

Clough, Katy; Lim, Eugene A.; DiNunno, Brandon S.
Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 09
DOI: 10.1088/1475-7516/2017/09/025

Inhomogeneous anisotropic cosmology
journal, October 2016

Kleban, Matthew; Senatore, Leonardo
Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 10
DOI: 10.1088/1475-7516/2016/10/022

Domain of Dependence
journal, February 1970

Geroch, Robert
Journal of Mathematical Physics, Vol. 11, Issue 2
DOI: 10.1063/1.1665157

Beginning inflation in an inhomogeneous universe
journal, September 2016

East, William E.; Kleban, Matthew; Linde, Andrei
Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 09
DOI: 10.1088/1475-7516/2016/09/010

Robustness of inflation to large tensor perturbations
journal, May 2018

Clough, Katy; Flauger, Raphael; Lim, Eugene A.
Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 05
DOI: 10.1088/1475-7516/2018/05/065

Closed universes: their future evolution and final state*
journal, September 1985

Barrow, J. D.; Tipler, F. J.
Monthly Notices of the Royal Astronomical Society, Vol. 216, Issue 2
DOI: 10.1093/mnras/216.2.395

The closed-universe recollapse conjecture
journal, December 1986

Barrow, J. D.; Galloway, G. J.; Tipler, F. J.
Monthly Notices of the Royal Astronomical Society, Vol. 223, Issue 4
DOI: 10.1093/mnras/223.4.835

Evolution of Binary Black-Hole Spacetimes
journal, September 2005

Pretorius, Frans
Physical Review Letters, Vol. 95, Issue 12
DOI: 10.1103/PhysRevLett.95.121101

Implications of Planck2015 for inflationary, ekpyrotic and anamorphic bouncing cosmologies
journal, January 2016

Ijjas, Anna; Steinhardt, Paul J.
Classical and Quantum Gravity, Vol. 33, Issue 4
DOI: 10.1088/0264-9381/33/4/044001

On mean curvature flow of spacelike hypersurfaces in asymptotically flat spacetimes
journal, August 1993

Ecker, Klaus
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 55, Issue 1
DOI: 10.1017/S1446788700031918

General Relativity
book, January 1984

Wald, Robert M.
DOI: 10.7208/chicago/9780226870373.001.0001

Existence of maximal surfaces in asymptotically flat spacetimes
journal, June 1984

Bartnik, Robert
Communications in Mathematical Physics, Vol. 94, Issue 2
DOI: 10.1007/bf01209300

Manifolds of positive Ricci curvature with almost maximal volume
journal, May 1994

Perelman, G.
Journal of the American Mathematical Society, Vol. 7, Issue 2
DOI: 10.1090/s0894-0347-1994-1231690-7

Time functions in numerical relativity: Marginally bound dust collapse
journal, April 1979

Eardley, Douglas M.; Smarr, Larry
Physical Review D, Vol. 19, Issue 8
DOI: 10.1103/physrevd.19.2239

Implications of Planck2015 for inflationary, ekpyrotic and anamorphic bouncing cosmologies
text, January 2015

Ijjas, Anna; Steinhardt, Paul J.
arXiv
DOI: 10.48550/arxiv.1512.09010

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Title: Asymptotic Behavior of Cosmologies with $$$$\Lambda >0$$$$ in $$2+1$$ Dimensions

Abstract

Citation Formats

Robustness of inflation to inhomogeneous initial conditions journal, September 2017

Inhomogeneous anisotropic cosmology journal, October 2016

Domain of Dependence journal, February 1970

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Time functions in numerical relativity: Marginally bound dust collapse journal, April 1979

Implications of Planck2015 for inflationary, ekpyrotic and anamorphic bouncing cosmologies text, January 2015

Robustness of inflation to inhomogeneous initial conditions
journal, September 2017

Inhomogeneous anisotropic cosmology
journal, October 2016

Domain of Dependence
journal, February 1970

Beginning inflation in an inhomogeneous universe
journal, September 2016

Robustness of inflation to large tensor perturbations
journal, May 2018

Closed universes: their future evolution and final state*
journal, September 1985

The closed-universe recollapse conjecture
journal, December 1986

Evolution of Binary Black-Hole Spacetimes
journal, September 2005

Implications of Planck2015 for inflationary, ekpyrotic and anamorphic bouncing cosmologies
journal, January 2016

On mean curvature flow of spacelike hypersurfaces in asymptotically flat spacetimes
journal, August 1993

General Relativity
book, January 1984

Existence of maximal surfaces in asymptotically flat spacetimes
journal, June 1984

Manifolds of positive Ricci curvature with almost maximal volume
journal, May 1994

Time functions in numerical relativity: Marginally bound dust collapse
journal, April 1979

Implications of Planck2015 for inflationary, ekpyrotic and anamorphic bouncing cosmologies
text, January 2015