http://arxiv.org/abs/1402.4045
We give the three-dimensional dynamical autonomous systems for most of the popular scalar field dark energy models including (phantom) quintessence, (phantom) tachyon, k-essence and general non-canonical scalar field models and change the dynamical variables from trivial variables $(x, y, \lambda)$ to observable related variables $(w_{\phi}, \Omega_{\phi}, \lambda)$. We show the intimate relationships between those scalar fields that the three-dimensional system of k-essence can reduce to (phantom) tachyon, general non-canonical scalar field can reduce to (phantom) quintessence and k-essence can also reduce to (phantom) quintessence for some special cases. For the applications of the three-dimensional dynamical systems, we investigate several special cases and give the exactly dynamical solutions in detail. Furthermore, we proved that the dark energy density parameter $\Omega_{\phi}$ would obey the same differential equation not only for all the scalar models in this paper but also for all the non-coupled dark energy models under the GR frame. We therefore get the result that, if we want to find a dark energy phenomenological model which possesses a stable attractor corresponding to current universe with $\Omega_{de}\sim 0.70$ and $\gamma_{de}\sim 0.1$ to solve or at least alleviate the cosmological coincidence problem without fine-tunings, we must consider the interaction between dark energy and other barotropic fluids. This result is valid for not only all the non-coupled dark energy models, but also for many modified gravity models as long as the energy density and the pressure of dark energy (or effective dark energy) satisfies the continuity equation in Eq.(67). In the end of this paper, we also raise a question about the possibility of the chaotic behavior in the spatially flat single scalar field FRW cosmological models in the presence of ordinary matter.
W. Fang, H. Tu, J. Huang, et. al.
Tue, 18 Feb 14
26/72
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