Attractor Solutions in Interacting Dark Energy Models

We investigate a cosmological model in which dark energy, represented by a quintessential scalar field, is coupled to a dark-matter perfect fluid in the spatially flat Friedmann-Robertson-Walker Universe. This allows an energy exchange in the dark sector which could happen both at early times before recombination era or at late times. We use the coupling function $Q=\gamma\rho_{dm}\dot{\varphi}$ which is induced by conformal transforming scalar-tensor and $f(R)$ gravity theories to Einstein frame. It is argued that there is a connection between this coupling function and $Q\propto \rho_{dm}H$. A dynamical analysis is used to show that there are early- and late-time attracting solutions for which the system evolves for a wide range of initial conditions. These attractors generalize the scaling solutions which have been already found in the non-interacting case.