Structure formation and the time dependence of quintessence

We discuss the influence of dark energy on structure formation, especially the effects on ${\sigma }_8.$ Our interest is particularly focused on quintessence models with a time-dependent equation of state and non-negligible quintessence component in the early universe. We obtain an analytic expression for ${\sigma }_8$ valid for a large class of dark energy models. We conclude that structure formation is a good indicator for the history of dark energy and use our results to set constraints on quintessence models.