Stability of curvature perturbation with new covariant form for   energy-momentum transfer in dark sector
  It was found that the model with interaction between cold dark matter (CDM) and dark energy (DE) proportional to the energy density of CDM $\rho_m$ and constant equation of state of DE $w_d$ suffered from instabilities of the density perturbations on the supper-Hubble scales. Here we suggest a new covariant model for the energy-momentum transfer between CDM and DE. Then using the covariant model, we analyze the evolution of density perturbations on the supper-Hubble scale. We find that the instabilities can be avoided in the model with constant $w_d$ and interaction proportional to $\rho_m$. Furthermore, we analyze the dominant non-adiabatic mode in the radiation era and find that the mode grows regularly. 
Cheng-Yi Sun, Yu Song and Rui-Hong Yue
gr-qc