The current accelerated expansion of our universe could be due to an unknown energy component with negative pressure (dark energy) or a modification to general relativity (modified gravity). On the other hand, recently warm dark matter (WDM) remarkably rose as an alternative of cold dark matter (CDM). Obviously, it is of interest to distinguish these different types of models. In fact, many attempts have been made in the literature. However, in the present work, we show that WDM, modified gravity and coupled CDM form a trinity, namely, they are indistinguishable by using the cosmological observations of both cosmic expansion history and growth history. Therefore, to break this degeneracy, the other complementary probes beyond the ones of cosmic expansion history and growth history are required.

13 pages, 4 figures, revtex4; v2: discussions added, Phys. Rev. D in press; v3: published version