Inhomogeneous anisotropic cosmology
Abstract
In homogeneous and isotropic FriedmannRobertsonWalker 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 3manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3manifolds 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 »
 Authors:

 New York Univ. (NYU), NY (United States). Center for Cosmology and Particle Physics
 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) (SC25)
 OSTI Identifier:
 1353055
 Alternate Identifier(s):
 OSTI ID: 1491173
 Grant/Contract Number:
 AC0276SF00515; PHY1214302; 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 14757516
 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:10.1088/14757516/2016/10/022.
Kleban, Matthew, & Senatore, Leonardo. Inhomogeneous anisotropic cosmology. United States. doi:10.1088/14757516/2016/10/022.
Kleban, Matthew, and Senatore, Leonardo. Wed .
"Inhomogeneous anisotropic cosmology". United States. doi:10.1088/14757516/2016/10/022. 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 FriedmannRobertsonWalker 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 3manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3manifolds 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 = {10.1088/14757516/2016/10/022},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 10,
volume = 2016,
place = {United States},
year = {2016},
month = {10}
}
Web of Science
Works referenced in this record:
Inflationary universe: A possible solution to the horizon and flatness problems
journal, January 1981
 Guth, Alan H.
 Physical Review D, Vol. 23, Issue 2
A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems
journal, February 1982
 Linde, A. D.
 Physics Letters B, Vol. 108, Issue 6
Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking
journal, April 1982
 Albrecht, Andreas; Steinhardt, Paul J.
 Physical Review Letters, Vol. 48, Issue 17
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
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
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
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
Domain of Dependence
journal, February 1970
 Geroch, Robert
 Journal of Mathematical Physics, Vol. 11, Issue 2
Hsurfaces in Lorentzian manifolds
journal, December 1983
 Gerhardt, Claus
 Communications in Mathematical Physics, Vol. 89, Issue 4
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
Time functions in numerical relativity: Marginally bound dust collapse
journal, April 1979
 Eardley, Douglas M.; Smarr, Larry
 Physical Review D, Vol. 19, Issue 8
Loitering universe
journal, January 1992
 Sahni, Varun; Feldman, Hume; Stebbins, Albert
 The Astrophysical Journal, Vol. 385
The closeduniverse 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
Causality and cosmic inflation
journal, December 1999
 Vachaspati, Tanmay; Trodden, Mark
 Physical Review D, Vol. 61, Issue 2
Manifolds of Positive Ricci Curvature with Almost Maximal Volume
journal, April 1994
 Perelman, G.
 Journal of the American Mathematical Society, Vol. 7, Issue 2
Works referencing / citing this record:
On the Problem of Initial Conditions for Inflation
journal, July 2018
 Linde, Andrei
 Foundations of Physics, Vol. 48, Issue 10
Anisotropic powerlaw inflation of the five dimensional scalar–vector and scalarKalb–Ramond model
journal, June 2018
 Do, Tuan Q.; Kao, W. F.
 The European Physical Journal C, Vol. 78, Issue 6
On the Problem of Initial Conditions for Inflation
journal, July 2018
 Linde, Andrei
 Foundations of Physics, Vol. 48, Issue 10
Anisotropic powerlaw inflation of the five dimensional scalar–vector and scalarKalb–Ramond model
journal, June 2018
 Do, Tuan Q.; Kao, W. F.
 The European Physical Journal C, Vol. 78, Issue 6