Parametrized post-Friedmann framework for interacting dark energy

Dark energy might directly interact with cold dark matter. However, in such a scenario, an early-time large-scale instability occurs occasionally, which may be due to the incorrect treatment for the pressure perturbation of dark energy as a nonadiabatic fluid. To avoid this nonphysical instability, we establish a new framework to correctly calculate the cosmological perturbations in the interacting dark energy models. Inspired by the well-known parametrized post-Friedmann approach, the condition of the dark energy pressure perturbation is replaced with the relationship between the momentum density of dark energy and that of other components on large scales. By reconciling the perturbation evolutions on the large and small scales, one can complete the perturbation equations system. The large-scale instability can be successfully avoided and the well-behaved density and metric perturbations are obtained within this framework. Our test results show that this new framework works very well and is applicable to all the interacting dark energy models.

Figure 1

The density perturbation evolutions at $k=0.1{\mathrm{Mpc}}^{-1}$ in the IDE model with $Q^{\mu }=3\beta H{\rho }_c{u}_c^{\mu }$ in the synchronous gauge. The upper panels are obtained by using the previous method, while the lower panels are obtained within the PPF framework proposed in this work.

Figure 2

The one- and two-dimensional posterior distributions for the parameters in the IDE model with $Q^{\mu }=3\beta H{\rho }_c{u}_c^{\mu }$.