Scaling Solutions in Robertson-Walker Spacetimes

Robert J. van den Hoogen; Alan A. Coley; David Wands

doi:10.1088/0264-9381/16/6/317

paper

Scaling Solutions in Robertson-Walker Spacetimes

arXiv:gr-qc/9901014 · doi:10.1088/0264-9381/16/6/317

Abstract

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 $V(ϕ)=V_0\e^{-κϕ}$. 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 $Ω_{ϕ} = 1$ ( $γ < 2/3, κ^{2} < 3 γ$ and $γ > 2/3, κ^{2} < 2$ ). 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 $Ω_{ϕ} = 3 γ / κ^{2}$ ( $γ < 2/3, κ^{2} > 3 γ$ ). 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 $Ω_{ϕ} = 2/ κ^{2}$ ( $γ > 2/3, κ^{2} > 2$ ). We find that solutions with $Ω_{ϕ} = 0$ are never late-time attractors.

8 pages, no figures, latex with revtex

Scaling Solutions in Robertson-Walker Spacetimes

Abstract

References in corpus (9)

Cited by in corpus (68)