On coincidence problem in ELKO dark energy model

General Relativity and Gravitation (Impact Factor: 1.77). 09/2011; 44(9). DOI: 10.1007/s10714-012-1392-x
Source: arXiv


We study the critical points of a universe dominated by ELKO spinor field
dark energy and a barotropic matter without considering a specific potential or
interaction. The coincidence problem and attractor solutions are discussed at
late time, and it is shown that the coincidence problem can not be solved in
this model.

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Available from: Hossein Mohseni Sadjadi, Aug 19, 2014
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    • "Such a search for adequate variables depends in general on the structure of the physical quantities involved, like the energy density, pressure and Friedmann constraints. In some recent works [44] [45] [46], different choices of variables for interacting systems concerning the ELKO field have shown that there are no stable points in order to explain the cosmic coincidence problem. In [47] it was proposed a new method of analysis based on a constant parameter that leads to stable points under some conditions. "
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    ABSTRACT: In this work it has been developed a new approach to study the stability of a system composed by an ELKO field interacting with dark matter, which could give some contribution in order to alleviate the cosmic coincidence problem. It is assumed that the potential that characterizes the ELKO field is not specified, but it is related to a constant parameter $\delta$. The strength of the interaction between the matter and the ELKO field is characterized by a constant parameter $\beta$ and it is also assumed that both the ELKO field as the matter energy density are related to their pressures by equations of state parameters $\omega_\phi$ and $\omega_m$, respectively. The system of equations is analysed by a dynamical system approach. It was found out the conditions of stability between the parameters $\delta$ and $\beta$ in order to have stable fixed points for the system for different values of the equation of state parameters $\omega_\phi$ and $\omega_m$, and the results are presented in form of tables. The possibility of decay of Elko field into dark matter or vice verse can be read directly from the tables, since the parameters $\delta$ and $\beta$ satisfy some inequalities. This opens the possibility to constrain the potential in order to have a stable system for different interactions terms between the Elko field and dark matter. The cosmic coincidence problem can be alleviated for some specific relations between the parameters of the model.
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    Hao Wei ·
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    ABSTRACT: Recently, Geng et al. proposed to allow a non-minimal coupling between quintessence and gravity in the framework of teleparallel gravity, motivated by the similar one in the framework of General Relativity (GR). They found that this non-minimally coupled quintessence in the framework of teleparallel gravity has a richer structure, and named it "teleparallel dark energy". In the present work, we note that there might be a deep and unknown connection between teleparallel dark energy and Elko spinor dark energy. Motivated by this observation and the previous results of Elko spinor dark energy, we try to study the dynamics of teleparallel dark energy. We find that there exist only some dark-energy-dominated de Sitter attractors. Unfortunately, no scaling attractor has been found, even when we allow the possible interaction between teleparallel dark energy and matter. However, we note that $w$ at the critical points is in agreement with observations (in particular, the fact that $w=-1$ independently of $\xi$ is a great advantage).
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    ABSTRACT: In this work, we have studied the Brans-Dicke (BD) cosmology in anisotropic models. We present three dimensional dynamical system describing the evolution of anisotropic models containing perfect fluid and BD scalar field with self-interacting potential. The relevant equations have been transformed into the dynamical system. The critical points and the corresponding eigen values have been found in radiation, dust, dark energy, $\Lambda$CDM and phantom phases of the universe. The natures and the stability around the critical points have also been investigated.
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