Statefinder diagnostic for coupled quintessence
  The problem of the cosmic coincidence is a longstanding puzzle. This conundrum may be solved by introducing a coupling between the two dark sectors. In this Letter, we study two cases of the coupled quintessence scenario. $(a)$ Assume that the mass of dark matter particles depends exponentially on the scalar field associated to dark energy and meanwhile the scalar field evolves in an exponential potential; $(b)$ Assume that the mass of dark matter particles depends on a power law function of the scalar field and meanwhile the scalar field evolves in a power law potential. Since the dynamics of this system is dominated by an attractor solution, the mass of dark matter particles is forced to change with time as to ensure that the ratio between the energy densities of dark matter and dark energy becomes a constant at late times, and one thus solve the cosmic coincidence problem naturally. We perform a statefinder diagnostic to both cases of this coupled quintessence scenario. It is shown that the evolving trajectory of this scenario in the $s-r$ diagram is quite different from those of other dark energy models. 
Xin Zhang