Coupled quintessence with a generalized interaction term

We investigate a cosmological model in which dark energy, represented by a quintessential scalar field, is directly coupled to a dark-matter perfect fluid. We are interested in solutions of cosmological relevance, namely those for which a dark-matter-dominated era long enough to allow for structure formation is followed by an era of accelerated expansion driven by dark energy. For the coupling between these two dark components of the Universe, we choose forms that generalize the one most commonly used in the literature. Resorting to powerful methods of qualitative analysis of dynamical systems, we show that, for certain generalized forms of the coupling, final states of our coupled quintessential model correspond to solutions in which the evolution of the Universe is completely dominated by dark energy. In this case, there are no scaling solutions. Interestingly, however, for certain values of a relevant parameter, during the approach to the final state of evolution, the cosmological parameters change so slowly that, for all practical purposes, the solution appears to be stuck in a state corresponding to a scaling solution.