Dynamics of Quintessence Models of Dark Energy with Exponential Coupling to the Dark Matter

We explore quintessence models of dark energy which exhibit non-minimal coupling between the dark matter and the dark energy components of the cosmic fluid. The kind of coupling chosen is inspired in scalar-tensor theories of gravity. We impose a suitable dynamics of the expansion allowing to derive exact Friedmann-Robertson-Walker solutions once the coupling function is given as input. Self-interaction potentials of single and double exponential types emerge as result of our choice of the coupling function. The stability and existence of the solutions is discussed in some detail. Although, in general, models with appropriated interaction between the components of the cosmic mixture are useful to handle the coincidence problem, in the present study the coincidence can not be evaded due to the choice of the solution generating ansatz.