Testing the interaction model with cosmological data and gamma-ray bursts

We use the new gamma-ray bursts (GRBs) data, combined with the baryon acoustic oscillation(BAO) observation from the spectroscopic Sloan Digital Sky Survey (SDSS) data release, the newly obtained $A$ parameter at $z=0.6$ from the WiggleZ Dark Energy Survey, the cosmic microwave background (CMB) observations from the 7-Year Wilkinson Microwave Anisotropy Probe (WMAP7) results, and the type Ia supernovae (SNeIa) from Union2 set, to constrain a phenomenological model describing possible interactions between dark energy and dark matter, which was proposed to alleviate the coincidence problem of the standard $\Lambda$CDM model. By using the Markov Chain Monte Carlo (MCMC) method, we obtain the marginalized $1\sigma$ constraints $\Omega_{m}=0.2886\pm{0.0135}$, $r_m=-0.0047\pm{0.0046}$, and $w_X=-1.0658\pm{0.0564}$. We also consider other combinations of these data for comparison. These results show that: (1) the energy of dark matter is slightly transferring to that of dark energy; (2) even though the GRBs+BAO+CMB data present less stringent constraints than SNe+BAO+CMB data do, the GRBs can help eliminate the degeneracies among parameters.