Testing interacting dark matter and dark energy model with cosmological data

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 $Q = \gamma \rho_{\rm c}^{\alpha} \rho_{\rm d}^{\beta}$. 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 {\it 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.