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arXiv 1406.0128gr-qcastro-ph.COhep-th
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幂律动力学精髓的动力学研究

Full Investigation on the Dynamics of Power-Law Kinetic Quintessence

Wei Fang, Hong Tu, Ying Li, Jiasheng Huang, Chenggang Shu

摘要:

通过将势相关参数$Γ$($=\frac{V V''}{V'^2}$)作为另一个势参数$λ$($=\frac{V'}{κV^{3/2}}$)的函数,对幂律动力学本质$L(X, ϕ)=V(ϕ)(-X+X^2)$的动力学进行了全面的研究,相应地将对宇宙动力学系统的分析从二维扩展到三维.在已有文献的临界点基础上,我们发现了一个新的类deSitter主导吸引子(\textit{cp$6$}),并利用中心流形定理给出了它的稳定条件.对于暗能量主导解(\textit{cp$6$}和\textit{cp$7$}),由于声速为$c_s^2=0$或$c_s^2\ll 1$,所以可以与典型的精粹和快子模型区分开来。对于标度解(\textit{cp$8$}),非常有趣的是,声速$c_s^2=1/5$表现为普通物质时的声速。因此,我们指出,幂律动力学本质在冷暗物质功率谱和宇宙微波背景上应该有不同的特征,无论是在早期,当标量场是早期暗能量时,$Ω_ϕ$在高红移时是不可忽略的,还是在晚期,当它驱动加速膨胀时。我们甚至不知道这两个时代之间是否存在影响的退化。预计今后将对这些案件进行调查。

英文摘要:

We give a full investigation on the dynamics of power-law kinetic quintessence $L(X, ϕ)=V(ϕ)(-X+X^2)$ by considering the potential related parameter $Γ$($=\frac{V V''}{V'^2}$) as a function of another potential parameter $λ$($=\frac{V'}{κV^{3/2}}$), which correspondingly extends the analysis of the dynamical system of our universe from two-dimension to three-dimension. Beside the critical points found in previous papers, we find a new de-Sitter-like dominant attractor(\textit{cp$6$}) and give its stable condition using the center manifold theorem. For the dark energy dominant solution(\textit{cp$6$} and \textit{cp$7$}), it could be distinguished from canonical quintessence and tachyon models since the sound speed $c_s^2=0$ or $c_s^2\ll 1$. For the scaling solution (\textit{cp$8$}), it is very interesting that the sound speed $c_s^2=1/5$ while it behaves as ordinary matter. We therefore point out that the power-law kinetic quintessence should have different signatures on cold dark matter power spectrum and cosmic microwave background both at early time when this scalar field is an early dark energy with $Ω_ϕ$ being non-negligible at high redshift and at late time when it drives the accelerating expansion. We even do not know whether there are any degeneracies of the impacts between these two epoches. They are expected to be investigated in future.

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