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.
