Quintessential perturbations during scaling regime

A scalar field with an exponential potential allows a scaling solution where the density of the field follows the density of the dominating fluid. Such a scaling regime is often used as an important ingredient in many models of quintessence. We analyze the evolution of perturbations while the background follows the scaling. As a result, the perturbed scalar field also scales with the perturbed fluid, and the perturbations accompany the adiabatic mode as well as the isocurvature mode between the fluid and the field.