  Recently, Valiviita et al. (2008) have reported a large-scale early-time
instability in coupled dark energy and dark matter models. We take the same
form of energy-momentum exchange and specialise to the case when the
interaction rate is proportional to Hubble's parameter and the dark energy
density only. Provided the coupling is made small enough for a given equation
of state parameter, we show that the instability can be avoided. Expressions
are derived for non-adiabatic modes on super-horizon scales in both the
radiation and matter dominated regimes. We also examine the growth of dark
matter perturbations in the sub-horizon limit. There we find that the coupling
has almost no effect upon the growth of structure before dark energy begins to
dominate. Once the universe begins to accelerate, the relative dark matter
density fluctuations not only cease to grow as in uncoupled models, but
actually decay as the universe continues to expand.
