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We develop a theoretical method of constructing the quintessence potential directly from the effective equation of state function w (z), which describes the properties of the dark energy. We apply our method to four parametrizations of equation of state parameter and discuss the general features of the resulting potentials. In particular, it is shown that the constructed quintessence potentials are all in the form of a runaway type.
Guo et al. (2005) studied this question.