How to distinguish dark energy and modified gravity?

The current accelerated expansion of our universe could be due to an unknown energy component (dark energy) or a modification of general relativity (modified gravity). In the literature it has been proposed that combining the probes of the cosmic expansion history and growth history can distinguish between dark energy and modified gravity. In this work, without invoking nontrivial dark energy clustering, we show that the possible interaction between dark energy and dark matter could make the interacting dark model and the modified gravity model indistinguishable. An explicit example is also given. Therefore, it is required to seek some complementary probes beyond the ones of cosmic expansion history and growth history.