Effects of dark sectors' mutual interaction on the growth of structures

We present a general formalism to study the growth of dark matter perturbations when dark energy perturbations and interactions between dark sectors are present. We show that the dynamical stability on the growth of structure depends on the form of coupling between dark sectors. By taking the appropriate coupling which enables the stable growth of structure, we find that the effect of the interaction between dark sectors overwhelms that of dark energy perturbation on the growth of dark matter perturbation. Due to the influence of the interaction, the growth index can differ from the value without interaction by an amount up to the observational sensibility, which provides an opportunity to probe the interaction between dark sectors through future observations on the growth of structure.