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Exploring the full parameter space for an interacting dark energy model with recent observations including redshift-space distortions: Application of the parametrized post-Friedmann approach

Dark energy can modify the dynamics of dark matter if there exists a direct interaction between them. Thus a measurement of the structure growth, e.g., redshift-space distortions (RSD), can provide a powerful tool to constrain the interacting dark energy (IDE) models. For the widely studied $Q=3βHρ_{de}$ model, previous works showed that only a very small coupling ($β\sim\mathcal{O}(10^{-3})$) can survive in current RSD data. However, all these analyses had to assume $w>-1$ and $β>0$ due to the existence of the large-scale instability in the IDE scenario. In our recent work [Phys. Rev. D 90, 063005 (2014)], we successfully solved this large-scale instability problem by establishing a parametrized post-Friedmann (PPF) framework for the IDE scenario. So we, for the first time, have the ability to explore the full parameter space of the IDE models. In this work, we reexamine the observational constraints on the $Q=3βHρ_{de}$ model within the PPF framework. By using the Planck data, the baryon acoustic oscillation data, the JLA sample of supernovae, and the Hubble constant measurement, we get $β=-0.010^{+0.037}_{-0.033}$ ($1σ$). The fit result becomes $β=-0.0148^{+0.0100}_{-0.0089}$ ($1σ$) once we further incorporate the RSD data in the analysis. The error of $β$ is substantially reduced with the help of the RSD data. Compared with the previous results, our results show that a negative $β$ is favored by current observations, and a relatively larger interaction rate is permitted by current RSD data.