Exact models with non-minimal interaction between dark matter and (either phantom or quintessence) dark energy

A method for deriving Friedmann-Robertson-Walker (FRW) solutions developed in Chimento and Jakubi (1996 Int. J. Mod. Phys. D 5 71-84) is generalized to account for models with non-minimal coupling between the dark energy and the dark matter that are based on an action principle. New quintessence and phantom (flat) FRW solutions are found. Their physical significance is discussed. Additionally, the aforementioned method is modified so that, 'coincidence-free' solutions can be readily derived. Besides, we review some aspects of the phantom barrier crossing. In this regard we present a model which is free from the coincidence problem and, at the same time, does the crossing of the phantom barrier omega = -1 at late time. Finally, we give additional comments on the non-predictive properties of scalar-field cosmological models with or without energy transfer.