On the large-scale instability in interacting dark energy and dark matter fluids

Recently, Valiviita et al. [J. Cosmol. Astropart. Phys. 07 (2008) 020] 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 specialize 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 nonadiabatic modes on superhorizon scales in both the radiation and matter dominated regimes. We also examine the growth of dark matter perturbations in the subhorizon 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.