中文

Exponential potentials and cosmological scaling solutions

广义相对论与量子宇宙学 2011-05-05 v2 天体物理学 高能物理 - 唯象学

摘要

We present a phase-plane analysis of cosmologies containing a barotropic fluid with equation of state pγ=(γ1)ργp_\gamma = (\gamma-1) \rho_\gamma, plus a scalar field ϕ\phi with an exponential potential Vexp(λκϕ)V \propto \exp(-\lambda \kappa \phi) where κ2=8πG\kappa^2 = 8\pi G. In addition to the well-known inflationary solutions for λ2<2\lambda^2 < 2, there exist scaling solutions when λ2>3γ\lambda^2 > 3\gamma in which the scalar field energy density tracks that of the barotropic fluid (which for example might be radiation or dust). We show that the scaling solutions are the unique late-time attractors whenever they exist. The fluid-dominated solutions, where V(ϕ)/ργ0V(\phi)/\rho_\gamma \to 0 at late times, are always unstable (except for the cosmological constant case γ=0\gamma = 0). The relative energy density of the fluid and scalar field depends on the steepness of the exponential potential, which is constrained by nucleosynthesis to λ2>20\lambda^2 > 20. We show that standard inflation models are unable to solve this `relic density' problem.

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引用

@article{arxiv.gr-qc/9711068,
  title  = {Exponential potentials and cosmological scaling solutions},
  author = {Edmund J Copeland and Andrew R Liddle and David Wands},
  journal= {arXiv preprint arXiv:gr-qc/9711068},
  year   = {2011}
}

备注

6 pages RevTeX file with four figures incorporated (uses RevTeX and epsf). Matches published version