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Attractor solutions in scalar-field cosmology

Remmen, Grant N. and Carroll, Sean M. (2013) Attractor solutions in scalar-field cosmology. Physical Review D, 88 (8). Art. No. 083518. ISSN 1550-7998. doi:10.1103/PhysRevD.88.083518.

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Models of cosmological scalar fields often feature “attractor solutions” to which the system evolves for a wide range of initial conditions. There is some tension between this well-known fact and another well-known fact: Liouville’s theorem forbids true attractor behavior in a Hamiltonian system. In universes with vanishing spatial curvature, the field variables ϕ and ϕ˙ specify the system completely, defining an effective phase space. We investigate whether one can define a unique conserved measure on this effective phase space, showing that it exists for m^2ϕ^2 potentials and deriving conditions for its existence in more general theories. We show that apparent attractors are places where this conserved measure diverges in the ϕ-ϕ˙ variables and suggest a physical understanding of attractor behavior that is compatible with Liouville’s theorem.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Remmen, Grant N.0000-0001-6569-8866
Carroll, Sean M.0000-0002-4226-5758
Additional Information:© 2013 American Physical Society. Received 11 September 2013; published 18 October 2013. We thank Alan Guth and Chien-Yao Tseng for helpful conversations. G.N.R. is supported by a Hertz Graduate Fellowship and a NSF Graduate Research Fellowship. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1144469, by DOE Grant No. DE-FG02-92ER40701, and by the Gordon and Betty Moore Foundation through Grant No. 776 to the Caltech Moore Center for Theoretical Cosmology and Physics.
Group:Caltech Theory, Moore Center for Theoretical Cosmology and Physics
Funding AgencyGrant Number
Fannie and John Hertz FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-1144469
Department of Energy (DOE)DE-FG02-92ER40701
Gordon and Betty Moore Foundation776
Caltech Moore Center for Theoretical Cosmology and PhysicsUNSPECIFIED
Issue or Number:8
Classification Code:PACS: 98.80.Cq, 04.60.Kz, 95.36.+x
Record Number:CaltechAUTHORS:20131125-140730326
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:42689
Deposited On:05 Dec 2013 22:09
Last Modified:10 Nov 2021 16:26

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