http://arxiv.org/abs/1503.03678
The time evolution of the equation of state $w$ for quintessence models with a scalar field as dark energy is studied up to the third derivative ($d^3w/da^3$) with respect to scale factor $a$, in order to predict the future observations and specify the scalar potential parameters with the observables. The third derivative of $w$ for general potential $V$ was derived and applied to several types of potential. They are the inverse power-law ($V=M^{4+\alpha}/Q^{\alpha}$), exponential ($V=M^4\exp{(\beta M/Q)}$), mixed ( $V=M^{4+\gamma}\exp{(\beta M/Q)}/Q^{\gamma}$), cosine ($V=M^4(\cos (Q/f)+1)$) and the Gaussian types ($V=M^4\exp(-Q^2/\sigma^2)$), which are prototypical potentials for the freezing and thawing models. If the parameter number for a potential form is $ n$, it is necessary to find at least for $n+2$ independent observations to identify the potential form and the evolution of scalar field ($Q$ and $ \dot{Q} $). Such observations would be the values of $ \Omega_Q, w, dw/da. \cdots $, and $ dw^n/da^n$. From these specific potentials, we could predict the $ n+1 $ and higher derivative of $w$ ; $ dw^{n+1}/da^{n+1}, \cdots$. Since four of the above mentioned potentials have two parameters, it is necessary to calculate the third derivative of $w$ for them to estimate the predict values. If they are tested observationally, it will be understood whether the dark energy could be described by the scalar field with this potential. At least it will satisfy the necessary conditions.
Y. Muromachi, A. Okabayashi, D. Okada, et. al.
Fri, 13 Mar 15
2/50
Comments: 35pages
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