Attractor solutions in scalar-field cosmology

Grant N. Remmen and Sean M. Carroll
Phys. Rev. D 88, 083518 – Published 18 October 2013

Abstract

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 m2ϕ2 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 ϕϕ˙ variables and suggest a physical understanding of attractor behavior that is compatible with Liouville’s theorem.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 11 September 2013

DOI:https://doi.org/10.1103/PhysRevD.88.083518

© 2013 American Physical Society

Authors & Affiliations

Grant N. Remmen* and Sean M. Carroll

  • California Institute of Technology, Pasadena, California 91125, USA

  • *gremmen@theory.caltech.edu
  • seancarroll@gmail.com

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 88, Iss. 8 — 15 October 2013

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×