The coincidence problem in linear dark energy models

P. P. Avelino

doi:10.1016/j.physletb.2005.02.037

paper

The coincidence problem in linear dark energy models

arXiv:astro-ph/0411033 · doi:10.1016/j.physletb.2005.02.037

Abstract

We show that a solution to the the coincidence problem can be found in the context of a generic class of dark energy models with a scalar field, $ϕ$ , with a linear effective potential $V (ϕ)$ . We determine the fraction, $f$ , of the total lifetime of the universe, $t_{U}$ , which lies within the interval $[t_{0} - Δ t_{A}, t_{0} + Δ t_{A}]$ , where $t_{0}$ is the age of the universe at the present time, $Δ t_{A} \equiv t_{0} - t_{A}$ and $t_{A}$ is the age of the universe when it starts to accelerate. We find that if we require $f$ to be larger than 0.1 (0.01) then $1+ω_{\phi0} \gapp 2 \times 10^{-2}$ ( $1 \times 1 0^{- 3}$ ), where $ω_{ϕ} \equiv p_{ϕ} / ρ_{ϕ}$ . These results depend mainly on the linearity of the scalar field potential for $-V(ϕ_0) \lapp V(ϕ) \lapp V(ϕ_0)$ and are weakly dependent on the specific form of $V (ϕ)$ outside this range. We also show that if $ω_{ϕ 0}$ is close to -1 then $ω_{ϕ 0} + 1 \sim 1.6 (ω ~_{ϕ} + 1)$ , where $ω ~_{ϕ}$ is the weighted average value of $ω_{ϕ}$ in the time interval $[0, t_{0}]$ . We independently confirm current observational constraints on this class of models which give $ω_{\phi0} \lapp -0.6$ and $t_U \gapp 2.4 t_0$ at the $2 σ$ level.

7 pages, 3 figures, typos corrected, references added

The coincidence problem in linear dark energy models

Abstract

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