I. INTRODUCTION There has been convincing evidence indicating that our universe is experiencing an accelerated expansion[1]. In the framework of General Relativity, the impart of the acceleration of the universe is given by a kind of mysterious energy called dark energy(DE). One leading candidate of such DE is the cosmological constant. However, it is difficult to understand such a cosmological constant in terms of fundamental physics. Its value from observation is far below that calculated in quantum field theory, what is referred to as the cosmological constant problem. Moreover, using the cosmological constant to explain the DE, one is unavoidably led to the coincidence problem, namely, why the vacuum and matter energy densities are precisely of the same order today. Considering that DE contributes a significant fraction of the content of the universe, it is natural in the framework of field theory to consider its interactions with the remaining fields, as e.g., the other large fraction of the universe, the dark matter (DM). The possibility that DE and DM interact with each other has been widely discussed recently [2]-[23]. It has been shown that an appropriate interaction between DE and DM can provide a mechanism to alleviate the coincidence problem [2–6]. However, it has been suspected that the appearance of the coupling between dark sectors may lead to the curvature perturbation instability [7]. This problem was later clarified in [8] where it has been shown that the stability of curvature perturbation holds while appropriately choosing the forms of the interaction between dark sectors and the equations of state (EOS) of DE. Another possibility to cure the instability was suggested in [9]. Observational signatures on the dark sector mutual interaction have been found in the probes of the cosmic expansion history by using the WMAP, SNIa, BAO and SDSS data etc [11]-[17]. Interestingly it was disclosed that the late ISW effect has the unique ability to give insight into the coupling between dark sectors [17]. The small positive coupling indicates that there is energy transfer from DE to DM, what can help to alleviate the coincidence problem [17, 18]. To further unveil the nature of the interaction between DE and DM, we require complementary probes in addition to investigating the expansion history of the universe. It has been observed that the growth of cosmic structure can be influenced by a nonminimal interaction between dark sectors, what leaves a clear change in the growth index due to the coupling [19, 21]. Furthermore, it was suggested that the dynamical equilibrium of collapsed structures such as clusters would acquire a modification due to the coupling between DE and DM [22, 23]. Comparing the naive virial masses of a large sample of clusters with their masses estimated by X-ray and by weak lensing data, small positive coupling has been tightly constrained [23], what agrees with the results given in [17] from CMB. The redshift dependence of cluster number counts is another promising tool to discriminate different DE models. 2