Interacting Cosmological Fluids and the Coincidence Problem
  We examine the evolution of a universe comprising two interacting 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. Finally, we
investigate the general case in which the dark energy equation of state is p =
w*rho, where w is a constant, and show that periodic solutions can occur if w <
-1. We further demonstrate that the ratio of the dark matter to 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.
