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We derive slow-roll conditions for thawing quintessence. We solve the equation of motion of for a Taylor expanded potential (up to the quadratic order) in the limit where the equation of state w is close to -1 to derive the equation of state as a function of the scale factor. We find that the evolution of and hence w are described by only two parameters. The expression for w (a), which can be applied to general thawing models, coincides precisely with that derived recently by Dutta and Scherrer for hilltop quintessence. The consistency conditions of |w+1|1 are derived. The slow-roll conditions for freezing quintessence are also derived.
Takeshi Chiba (Thu,) studied this question.