Observational constraint on the interacting dark energy models including the Sandage-Loeb test

Two types of interacting dark energy models are investigated using the type Ia supernova (SNIa), observational data (OHD), cosmic microwave background shift parameter, and the secular Sandage-Loeb (SL) test. In the investigation, we have used two sets of parameter priors including WMAP-9 and Planck 2013. They have shown some interesting differences. We find that the inclusion of SL test can obviously provide a more stringent constraint on the parameters in both models. For the constant coupling model, the interaction term has been improved to be only a half of the original scale on corresponding errors. Comparing with only SNIa and OHD, we find that the inclusion of the SL test almost reduces the best-fit interaction to zero, which indicates that the higher-redshift observation including the SL test is necessary to track the evolution of the interaction. For the varying coupling model, data with the inclusion of the SL test show that the parameter at C.L. in Planck priors is , where the constant is characteristic for the severity of the coincidence problem. This indicates that the coincidence problem will be less severe. We then reconstruct the interaction , and we find that the best-fit interaction is also negative, similar to the constant coupling model. However, for a high redshift, the interaction generally vanishes at infinity. We also find that the phantom-like dark energy with is favored over the CDM model.