Coupled quintessence with a generalized interaction term

Abstract

We investigate a cosmological model in which dark energy, represented by a quintessential scalar field, is directly coupled to a dark-matter perfect fluid. 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 identify and analyze all solutions of cosmological relevance, that is, solutions for which a present era of accelerated expansion is preceded by a long enough dark-matter-dominated era. We show that, for certain generalized forms of the coupling, global attractors 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 critical points corresponding to scaling solutions. Interestingly, however, for certain values of a relevant parameter, during the approach to the global attractor the evolution of the cosmological parameters is so slow that, for all practical purposes, the solution appears to be stuck in a state corresponding to a scaling solution.