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Zlatev, I., Wang, L. and Steinhardt, P.J. (1999) Quintessence, Cosmic Coincidence, and the Cosmological Constant. Physical Review Letters, 82, 896. http://dx.doi.org/10.1103/PhysRevLett.82.896

has been cited by the following article:

  • TITLE: Quest for Potentials in the Quintessence Scenario

    AUTHORS: Tetsuya Hara

    KEYWORDS: Dark Energy, Quintessence, Thawing Model, Freezing Model

    JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.2, February 17, 2016

    ABSTRACT: 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 d2w/da2 in some parameters.