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Dark energy might interact with cold dark matter in a direct,nongravitational way. However, the usual interacting dark energy models (withconstant $w$) suffer from some catastrophic difficulties. For example, the$Q\propto\rho_{\rm c}$ model leads to an early-time large-scale instability,and the $Q\propto\rho_{\rm de}$ model gives rise to the future unphysicalresult for cold dark matter density (in the case of a positive coupling). Inorder to overcome these fatal flaws, we propose in this paper an interactingdark energy model (with constant $w$) in which the interaction term iscarefully designed to realize that $Q\propto\rho_{\rm de}$ at the early timesand $Q\propto\rho_{\rm c}$ in the future, simultaneously solving the early-timesuperhorizon instability and future unphysical $\rho_{\rm c}$ problems. Theconcrete form of the interaction term in this model is $Q=3\beta H\frac{\rho_{\rm{de}}\rho_{\rm{c}}}{\rho_{\rm{de}}+\rho_{\rm{c}}}$, where$\beta$ is the dimensionless coupling constant. We show that this model isactually equivalent to the decomposed new generalized Chaplygin gas (NGCG)model, with the relation $\beta=-\alpha w$. We calculate the cosmologicalperturbations in this model in a gauge-invariant way and show that thecosmological perturbations are stable during the whole expansion historyprovided that $\beta>0$. Furthermore, we use the Planck data in conjunctionwith other astrophysical data to place stringent constraints on this model(with eight parameters), and we find that indeed $\beta>0$ is supported by thejoint constraint at more than 1$\sigma$ level. The excellent theoreticalfeatures and the support from observations all indicate that the decomposedNGCG model deserves more attention and further investigation.

Large-scale stable interacting dark energy model: Cosmological perturbations and observational constraints