Exploring interacting holographic dark energy in a perturbed universe
  with parameterized post-Friedmann approach
  The model of holographic dark energy in which dark energy interacts with dark
matter is investigated in this paper. In particular, we consider the
interacting holographic dark energy model in the context of a perturbed
universe, which was never investigated in the literature. To avoid the
large-scale instability problem in the interacting dark energy cosmology, we
employ the generalized version of the parameterized post-Friedmann approach to
treat the dark energy perturbations in the model. We use the current
observational data to constrain the model. Since the cosmological perturbations
are considered in the model, we can then employ the redshift-space distortions
(RSD) measurements to constrain the model, in addition to the use of the
measurements of expansion history, which was either never done in the
literature. We find that, for both the cases with $Q=\beta H\rho_{\rm c}$ and
$Q=\beta H_0\rho_{\rm c}$, the interacting holographic dark energy model is
more favored by the current data, compared to the holographic dark energy model
without interaction. It is also found that, with the help of the RSD data, a
positive coupling $\beta$ can be detected at the $2.95\sigma$ statistical
significance for the case of $Q=\beta H_0\rho_{\rm c}$.
