Interacting parametrized post-Friedmann method

Abstract

We apply the interacting parametrized post-Friedmann (IPPF) method to coupled dark energy models where the interaction is proportional to dark matter density at background level. In the first case, the dark components are treated as fluids and the growth of dark matter perturbations only feel the interaction via the modification of background quantities provided dark matter follows geodesic. We also 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 fσ ₈(z) data points. The joint observational analysis of Planck+WP+JLA+BAO+HST+ RSD data leads to a coupling parameter, ξ _c=0.00140_{-0.00080}^{+0.00079} at 1σ level for vanishing momentum transfer potential. On the other hand, we deal with a coupled quintessence model which exhibits a violation of the equivalence principle coming form a coupling term in the modified Euler equation; as a result of that the local Hubble expansion rate and the effective gravitational coupling are both enhanced. Provided that the interaction is parallel to scalar field velocity the momentum transfer potential is switched on, leading to a lower interaction coupling ξ _c=0.00136_{-0.00073}^{+0.00080} at 1σ level when Planck+WP+JLA+BAO+HST+RSD data are combined. Besides, the CMB power spectrum shows up a correlation between the coupling parameter ξ _c and the position of acoustic peaks or their amplitudes. The first peak's height increases when ξ _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 than 10^{-2} h Mpc^{-1}, reducing its amplitude in relation to the vanilla model.