In this paper , we test the dark matter-dark energy interacting cosmological model with a dynamic equation of state w _ { DE } ( z ) = w _ { 0 } + w _ { 1 } z / ( 1 + z ) , using type Ia supernovae ( SNe Ia ) , Hubble parameter data , baryonic acoustic oscillation ( BAO ) measurements , and the cosmic microwave background ( CMB ) observation .
This interacting cosmological model has not been studied before .
The best-fitted parameters with 1 \sigma uncertainties are \delta = -0.022 \pm 0.006 , \Omega _ { DM } ^ { 0 } = 0.213 \pm 0.008 , w _ { 0 } = -1.210 \pm 0.033 and w _ { 1 } = 0.872 \pm 0.072 with \chi ^ { 2 } _ { min } / dof = 0.990 .
At the 1 \sigma confidence level , we find \delta < 0 , which means that the energy transfer prefers from dark matter to dark energy .
We also find that the SNe Ia are in tension with the combination of CMB , BAO and Hubble parameter data .
The evolution of \rho _ { DM } / \rho _ { DE } indicates that this interacting model is a good approach to solve the coincidence problem , because the \rho _ { DE } decrease with scale factor a .
The transition redshift is z _ { tr } = 0.63 \pm 0.07 in this model .