Interacting parametrized post-Friedmann method

We apply the interacting parametrized post-Friedmann (IPPF) method to a coupled dark energy model where the interaction is proportional to dark matter density at background level. In doing so, we perform a Markov Chain Monte-Carlo analysis which combines several cosmological probes including the cosmic microwave background (WMAP9+Planck) data, baryon acoustic oscillation (BAO) measurements, JLA sample of supernovae, Hubble constant (HST), and redshift-space distortion (RSD) measurements through the ${\rm f}\sigma_{8}{\rm (z)}$ data points. The joint observational analysis of ${\rm Planck+WP+JLA+BAO+HST+RSD}$ data leads to a coupling parameter, $\xi_{c}=0.00140_{-0.00080}^{+0.00079}$ at $1\sigma$ level for vanishing momentum transfer potential; this value is reduced a when the momentum transfer potential is switched on, giving $\xi_{c}=0.00136_{-0.00073}^{+0.00080}$ at $1\sigma$ level. The CMB power spectrum shows up a correlation between the coupling parameter $\xi_{c}$ and the position of acoustic peaks or their amplitudes. The first peak's height increases when $\xi_{c}$ takes larger values and its position is shifted. We also obtain the matter power spectrum may be affected by the strength of interaction coupling over scales bigger that $10^{-2} {\rm h~ Mpc^{-1}}$, reducing its amplitude in relation to the vanilla model.