1999/01/07 by Robert J. van den Hoogen, Alan A. Coley, David Wands · 1 citation
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1088/0264-9381/16/6/317
published as Class.Quant.Grav.16:1843-1851,1999 · 8 pages, no figures, latex with revtex
arxiv created 1999/01/07 · arxiv updated 2009/11/30
We investigate the stability of cosmological scaling solutions describing a barotropic fluid with p=(γ-1)ρ and a non-interacting scalar field ϕ with an exponential potential V(ϕ)=V0\e-κϕ. We study homogeneous and isotropic spacetimes with non-zero spatial curvature and find three possible asymptotic future attractors in an ever-expanding universe. One is the zero-curvature power-law inflation solution where Ωϕ=1 (γ<2/3,κ2<3γ and γ>2/3,κ2<2). Another is the zero-curvature scaling solution, first identified by Wetterich, where the energy density of the scalar field is proportional to that of matter with Ωϕ=3γ/κ2 (γ<2/3,κ2>3γ). We find that this matter scaling solution is unstable to curvature perturbations for γ>2/3. The third possible future asymptotic attractor is a solution with negative spatial curvature where the scalar field energy density remains proportional to the curvature with Ωϕ=2/κ2 (γ>2/3,κ2>2). We find that solutions with Ωϕ=0 are never late-time attractors.