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arXiv · 1309.2611

Attractor Solutions in Scalar-Field Cosmology

Grant N. Remmen·Sean M. Carroll
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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,\dotϕ) 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,\dotϕ) variables and suggest a physical understanding of attractor behavior that is compatible with Liouville's theorem.

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Grant N. Remmen, Sean M. Carroll. 2013-09-10. Attractor Solutions in Scalar-Field Cosmology. https://doi.org/10.1103/physrevd.88.083518

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