Quintom models with an equation of state crossing -1

Wen Zhao; Yang Zhang

doi:10.1103/PhysRevD.73.123509

paper

Quintom models with an equation of state crossing -1

arXiv:astro-ph/0604460 · doi:10.1103/PhysRevD.73.123509

Abstract

In this paper, we investigate a kind of special quintom model, which is made of a quintessence field $ϕ_{1}$ and a phantom field $ϕ_{2}$ , and the potential function has the form of $V (ϕ_{1}^{2} - ϕ_{2}^{2})$ . This kind of quintom fields can be separated into two kinds: the hessence model, which has the state of $ϕ_{1}^{2} > ϕ_{2}^{2}$ , and the hantom model with the state $ϕ_{1}^{2} < ϕ_{2}^{2}$ . We discuss the evolution of these models in the $ω$ - $ω^{'}$ plane ( $ω$ is the state equation of the dark energy, and $ω^{'}$ is its time derivative in unites of Hubble time), and find that according to $ω > - 1$ or $< - 1$ , and the potential of the quintom being climbed up or rolled down, the $ω$ - $ω^{'}$ plane can be divided into four parts. The late time attractor solution, if existing, is always quintessence-like or $Λ$ -like for hessence field, so the Big Rip doesn't exist. But for hantom field, its late time attractor solution can be phantom-like or $Λ$ -like, and sometimes, the Big Rip is unavoidable. Then we consider two special cases: one is the hessence field with an exponential potential, and the other is with a power law potential. We investigate their evolution in the $ω$ - $ω^{'}$ plane. We also develop a theoretical method of constructing the hessence potential function directly from the effective equation of state function $ω (z)$ . We apply our method to five kinds of parametrizations of equation of state parameter, where $ω$ crossing -1 can exist, and find they all can be realized. At last, we discuss the evolution of the perturbations of the quintom field, and find the perturbations of the quintom $δ_{Q}$ and the metric $Φ$ are all finite even if at the state of $ω = - 1$ and $ω^{'} \neq = 0$ .

28 pages, 8 figures. Style is revised

Quintom models with an equation of state crossing -1

Abstract

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