We investigate the model of dark matter-dark energy ( DM-DE ) interaction with coupling strength proportional to the multiplication of dark sector densities with different power indices Q = \gamma \rho _ { c } ^ { \alpha } \rho _ { d } ^ { \beta } .
We first investigate the modification of the cosmic expansion history , and then further develop the formalism to take into account the cosmological perturbations and dark matter temperature evolution .
We then use the latest observational cosmology data , including cosmic microwave background ( CMB ) data , baryon acoustic oscillations ( BAO ) data , redshift-space distortion ( RSD ) data and Type Ia supernovae ( SNe ) data to constrain the model parameters .
We find in the phantom region , a positive \alpha is preferred by the data above 2 \sigma statistic significance .
If we choose the power indices to be integers or half-integers for plausible physics of particle interaction , the allowed values within 1 \sigma confidence regions are \alpha = 0.5 and \beta = 0 , 0.5 , 1 .
The inclusion of BAO and RSD data from large-scale structure and SNe data improves the constraints significantly .
Our model predicts lower values of f ( z ) \sigma _ { 8 } ( z ) at z < 1 comparing to \Lambda CDM model , which alleviates the tension of \Lambda CDM with various RSD data from optical galaxy surveys .
Overall , the DM-DE interaction model is consistent with the current observational data , especially providing a better fit to the RSD data .