  Dark energy might directly interact with cold dark matter. However, in such a
scenario, an early-time large-scale instability occurs occasionally, which may
be due to the incorrect treatment for the pressure perturbation of dark energy
as a nonadiabatic fluid. To avoid this nonphysical instability, we establish a
new framework to correctly calculate the cosmological perturbations in the
interacting dark energy models. Inspired by the well-known parametrized
post-Friedmann approach, the condition of the dark energy pressure perturbation
is replaced with the relationship between the momentum density of dark energy
and that of other components on large scales. By reconciling the perturbation
evolutions on the large and small scales, one can complete the perturbation
equations system. The large-scale instability can be successfully avoided and
the well-behaved density and metric perturbations are obtained within this
framework. Our test results show that this new framework works very well and is
applicable to all the interacting dark energy models.
