Slow-Roll Thawing Quintessence

We derive slow-roll conditions for thawing quintessence. We solve the equation of motion of $\phi$ 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 $\phi$ 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 $|w+1|\ll 1$ are derived. The slow-roll conditions for freezing quintessence are also derived.