skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Inhomogeneous anisotropic cosmology

Abstract

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 arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat'' or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energymore » or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.« less

Authors:
 [1];  [2]
  1. New York Univ. (NYU), NY (United States). Center for Cosmology and Particle Physics
  2. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics and Dept. of Physics; SLAC National Accelerator Lab., Menlo Park, CA (United States). Kavli Inst. for Particle Astrophysics and Cosmology
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States)
Sponsoring Org.:
National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1353055
Alternate Identifier(s):
OSTI ID: 1491173
Grant/Contract Number:  
AC02-76SF00515; PHY-1214302; SC0008078
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Cosmology and Astroparticle Physics
Additional Journal Information:
Journal Volume: 2016; Journal Issue: 10; Journal ID: ISSN 1475-7516
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; gravity; initial conditions and eternal universe; cosmological simulations; inflation

Citation Formats

Kleban, Matthew, and Senatore, Leonardo. Inhomogeneous anisotropic cosmology. United States: N. p., 2016. Web. doi:10.1088/1475-7516/2016/10/022.
Kleban, Matthew, & Senatore, Leonardo. Inhomogeneous anisotropic cosmology. United States. doi:10.1088/1475-7516/2016/10/022.
Kleban, Matthew, and Senatore, Leonardo. Wed . "Inhomogeneous anisotropic cosmology". United States. doi:10.1088/1475-7516/2016/10/022. https://www.osti.gov/servlets/purl/1353055.
@article{osti_1353055,
title = {Inhomogeneous anisotropic cosmology},
author = {Kleban, Matthew and Senatore, Leonardo},
abstractNote = {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 arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat'' or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.},
doi = {10.1088/1475-7516/2016/10/022},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 10,
volume = 2016,
place = {United States},
year = {2016},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Inflationary universe: A possible solution to the horizon and flatness problems
journal, January 1981


Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking
journal, April 1982


Chaotic inflation
journal, September 1983


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

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


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

Domain of Dependence
journal, February 1970

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

H-surfaces in Lorentzian manifolds
journal, December 1983

  • Gerhardt, Claus
  • Communications in Mathematical Physics, Vol. 89, Issue 4
  • DOI: 10.1007/BF01214742

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

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


Loitering universe
journal, January 1992

  • Sahni, Varun; Feldman, Hume; Stebbins, Albert
  • The Astrophysical Journal, Vol. 385
  • DOI: 10.1086/170910

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

Causality and cosmic inflation
journal, December 1999


Manifolds of Positive Ricci Curvature with Almost Maximal Volume
journal, April 1994

  • Perelman, G.
  • Journal of the American Mathematical Society, Vol. 7, Issue 2
  • DOI: 10.2307/2152760

    Works referencing / citing this record:

    On the Problem of Initial Conditions for Inflation
    journal, July 2018


    Anisotropic power-law inflation of the five dimensional scalar–vector and scalar-Kalb–Ramond model
    journal, June 2018


    On the Problem of Initial Conditions for Inflation
    journal, July 2018


    Anisotropic power-law inflation of the five dimensional scalar–vector and scalar-Kalb–Ramond model
    journal, June 2018