Cosmological constraints on coupled dark energy

The coupled dark energy model provides a possible approach to mitigate the coincidence problem of cosmological standard model. Here, the coupling term is assumed as $\bar{Q}=3H\xi_x\bar{\rho}_x$, which is related to the interaction rate and energy density of dark energy. We derive the background and perturbation evolution equations for several coupled models. Then, we test these models by currently available cosmic observations which include cosmic microwave background radiation from Planck 2015, baryon acoustic oscillation, type Ia supernovae, $f\sigma_8(z)$ data points from redshift-space distortions, and weak gravitational lensing. The constraint results tell us there is no evidence of interaction at 2$\sigma$ level, it is very hard to distinguish different coupled models from other ones.