We investigate observational constraints on the Dvali, Gabadadze and Porrati （DGP） model with Gamma-ray bursts （GRBs） at high redshift obtained directly from the Union2 Type Ia supernovae data set. With cosmology-independent GRBs, the Union2 set, as well as the cosmic microwave background observation from the WMAP7 result, the baryon acoustic oscillation, the baryon mass fraction in clus- ters and the observed H（z） data, we obtain that the best-fit values of the DGP model are {ΩM0,Ωrc} = {0.235^＋0.015-0.14, 0.138^＋0.o51-0.048}, which favor a flat universe, and the transition redshift of the DGP model is ZT=0.67^＋0.03-0.04.These results lead to more stringent constraints than the previous results for the DGP model.
We use the latest data to investigate observational constraints on the new generalized Chaplygin gas （NGCG） model. Using the Markov Chain Monte Carlo method, we constrain the NGCG model with type Ia supernovae from the Union2 set （557 data）, the usual baryonic acoustic oscillation （BAO） observation from the spectroscopic Sloan Digital Sky Survey data release 7 galaxy sample, the cosmic mi- crowave background observation from the 7-year Wilkinson Microwave Anisotropy Probe results, newly revised data on H（z）, as well as a value of θBAO （Z = 0.55） = （3.90° ±0.38°） for the angular BAO scale. The constraint results for the NGCG model are ωX=-1.0510＋0.1563-0.1685（1σ）＋0.2226-0.2398（2σ）,η=1.0117＋0.0469-0.0502（1σ）＋0.0693-0.0716（2σ）and ΩX=0.7297＋0.0229-0.0276（1σ）＋0.0329-0.0402（2σ）, which give a rather stringent constraint. From the results, we can see that a phantom model is slightly favored and the proba- bility that energy transfers from dark matter to dark energy is a little larger than the inverse.
