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:: 2020-03-11

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.

Copy to clipboard


                    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

Copy to clipboard


                    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.

Copy to clipboard


                    
@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         = {2020},

  month        = {3}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/s00220-020-03706-3

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 2 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

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

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
DOI: 10.1103/PhysRevD.28.2118

Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes
journal, January 1991

Ecker, Klaus; Huisken, Gerhard
Communications in Mathematical Physics, Vol. 135, Issue 3
DOI: 10.1007/BF02104123

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

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

Similar Records in DOE PAGES and OSTI.GOV collections:

Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant

Journal Article Wald, R M - Phys. Rev. D; (United States)

We examine the late-time behavior of initially expanding homogeneous cosmological models satisfying Einstein's equation with a positive cosmological constant ..lambda... It is shown that such models of all Bianchi types except IX exponentially evolve toward the de Sitter solution, with time scale (3/..lambda..)/sup 1/2/. The behavior of Bianchi type-IX universes is similar, provided that ..lambda.. is sufficiently large compared with spatial-curvature terms. Thus, a positive cosmological constant provides an effective means of isotropizing homogeneous universes.
https://doi.org/10.1103/PhysRevD.28.2118
Inflation in Flatland

Journal Article Hinterbichler, Kurt ; Joyce, Austin ; Khoury, Justin - Journal of Cosmology and Astroparticle Physics

We investigate the symmetry structure of inflation in 2+1 dimensions. In particular, we show that the asymptotic symmetries of three-dimensional de Sitter space are in one-to-one correspondence with cosmological adiabatic modes for the curvature perturbation. In 2+1 dimensions, the asymptotic symmetry algebra is infinite-dimensional, given by two copies of the Virasoro algebra, and can be traced to the conformal symmetries of the two-dimensional spatial slices of de Sitter. We study the consequences of this infinite-dimensional symmetry for inflationary correlation functions, finding new soft theorems that hold only in 2+1 dimensions. Expanding the correlation functions as a power series in themore »« less
https://doi.org/10.1088/1475-7516/2017/01/044
Inhomogeneous anisotropic cosmology

Journal Article Kleban, Matthew ; Senatore, Leonardo ; Kavli Institute for Particle Astrophysics and Cosmology, Stanford University and SLAC,2575 Sand Hill Road, M/S 29, Menlo Park, CA 94025 - Journal of Cosmology and Astroparticle Physics

In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with “flat” (including toroidal) and “open” (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuationsmore »« less
https://doi.org/10.1088/1475-7516/2016/10/022
Inhomogeneous anisotropic cosmology

Journal Article Kleban, Matthew ; Senatore, Leonardo - Journal of Cosmology and Astroparticle Physics

In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here in this paper, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with "flat'' (including toroidal) and "open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarilymore »« less
Cited by 46
https://doi.org/10.1088/1475-7516/2016/10/022

Full Text Available
Asymptotically (anti)-de Sitter solutions in Gauss-Bonnet gravity without a cosmological constant

Journal Article Dehghani, M H ; Institute for Studies in Theoretical Physics and Mathematics ; Research Institute for Astrophysics and Astronomy of Maragha, P.O. Box 55134-441, Maragha - Physical Review. D, Particles Fields

In this paper I show that one can have asymptotically de Sitter, anti-de Sitter (AdS), and flat solutions in Gauss-Bonnet gravity without a cosmological constant term in field equations. First, I introduce static solutions whose three surfaces at fixed r and t have constant positive (k=1), negative (k=-1), or zero (k=0) curvature. I show that for k={+-}1 one can have asymptotically de Sitter, AdS, and flat spacetimes, while for the case of k=0, one has only asymptotically AdS solutions. Some of these solutions present naked singularities, while some others are black hole or topological black hole solutions. I also findmore »« less
https://doi.org/10.1103/PhysRevD.70.064019

Similar Records

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

Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant journal, October 1983

Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes journal, January 1991

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

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

Robustness of inflation to inhomogeneous initial conditions
journal, September 2017

Inhomogeneous anisotropic cosmology
journal, October 2016

Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant
journal, October 1983

Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes
journal, January 1991

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

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