Interacting cosmological fluids and the coincidence problem

We examine the evolution of a universe comprising two fluids which interact via a term proportional to the product of their densities. In the case of two matter fluids, it is shown that the ratio of the densities tends to a constant after an initial cooling-off period. We then obtain a complete solution for the cosmological constant (w=-1) scenario and show that periodic solutions can occur if w<-1. We further demonstrate that the ratio of the dark matter and dark energy densities is confined to a bounded interval and that this ratio can be $O(1)$ at infinitely many times in the history of the universe, thus solving the coincidence problem. Finally, we show that, for a certain choice of parameters, the model is a viable fit to observational constraints, and we give a detailed discussion of the past and future evolution of the universe in this particular case.