The time evolution of the equation of state w for quintessence scenario with a scalar field as dark energy is studied up to the third derivative (d3w/da3) with respect to the scale factor a, in order to predict the fu...The time evolution of the equation of state w for quintessence scenario with a scalar field as dark energy is studied up to the third derivative (d3w/da3) with respect to the 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 is derived and applied to several types of potentials. They are the inverse power-law (V = M4 + α/Qα), the exponential , the mixed , the cosine and the Gaussian types , 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 for0m and the evolution of the scalar field (Q and ). Such observations would be the values of ΩQ, w, dw/da, ???, and dwn/dan. From these specific potentials, we can predict the n + 1 and higher derivative of w;dwn + 1/dan + 1, ???. 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 under- stood whether the dark energy could be described by the scalar field with this potential. At least it will satisfy the necessary conditions. Numerical analysis for d3w/da3 is made under some specified parameters in the investigated potentials, except the mixed one. It becomes possible to distinguish the potentials by the accurate observing dw/da and d<sup>2</sup>w/da<sup>2</sup> in some parameters.展开更多
文摘The time evolution of the equation of state w for quintessence scenario with a scalar field as dark energy is studied up to the third derivative (d3w/da3) with respect to the 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 is derived and applied to several types of potentials. They are the inverse power-law (V = M4 + α/Qα), the exponential , the mixed , the cosine and the Gaussian types , 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 for0m and the evolution of the scalar field (Q and ). Such observations would be the values of ΩQ, w, dw/da, ???, and dwn/dan. From these specific potentials, we can predict the n + 1 and higher derivative of w;dwn + 1/dan + 1, ???. 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 under- stood whether the dark energy could be described by the scalar field with this potential. At least it will satisfy the necessary conditions. Numerical analysis for d3w/da3 is made under some specified parameters in the investigated potentials, except the mixed one. It becomes possible to distinguish the potentials by the accurate observing dw/da and d<sup>2</sup>w/da<sup>2</sup> in some parameters.
