Probing the interaction between dark energy and dark matter with the parametrized post-Friedmann approach

In the current universe, the dominant energy components are dark energy and dark matter. There is a longstanding conjecture that there might be some direct coupling between dark energy and dark matter （for a recent review, see ref. [1]）. The advantages for considering such a possibility include, for example, those that it can alleviate the ＂cosmic coincidence＂ puzzle, can avoid the ＂big rip＂ in a phantom scenario, and so on. We call the scenario in which dark energy directly in- teracts with dark matter the ＂interacting dark energy＂ （IDE） scenario. Actually, besides the above reasons of theoretical aspect, one should be more concerned with the observational issue： How can we detect this interaction （this is essentially a kind of ＂fifth force＂） or falsify this scenario by using the observations？ This requires us to be able to calculate how it affects the cosmological evolution, including both aspects of expansion history and growth of structure.