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Dark energy might interact with dark matter in a direct, non-gravitationalway, which can help remedy several theoretical defects. In order to find outthe properties of interacting dark energy models, it is necessary toinvestigate the cosmological perturbations in detail. However, due to theimproper use of pressure perturbation of dark energy, a large-scale instabilityat the early stage occurs occasionally. In recent years, parametrizedpost-Friedmann approach has been used to calculate the perturbation equationsin the interacting dark energy scenario. Under this framework, the dark energypressure perturbation was replaced by the relationship between the momentumdensity of dark energy and other components on a large scale. However, thispaper shows that if the interaction terms are related to the velocityperturbation of dark energy, the density perturbation of dark matter and thematter power spectrum will diverge when the equation of state parameter of darkenergy $w$ is close to $-1$. A simple parameterization steering clear of thisproblem is proposed in this paper which is a more general form and can beapplied to explore the interaction between dark matter and dark energy by usingvarious cosmological data.

Revisiting the Instability Problem of Interacting Dark Energy Model in the Parametrized Post-Friedmann Framework