Evolution of large-scale perturbations in quintessence models

We carry out a comprehensive study of the dynamics of large-scale perturbations in quintessence scenarios. We model the contents of the Universe by a perfect fluid with equation of state w(f) and a scalar field Q with potential V(Q). We are able to reduce the perturbation equations to a system of four first-order equations. During each of the five main regimes of quintessence field behavior, these equations have constant coefficients, enabling an analytic solution of the perturbation evolution by eigenvector decomposition. We determine these solutions and discuss their main properties.