Cosmic constraint to DGP brane model: Geometrical and dynamical perspectives

In this paper, the Dvali-Gabadadze-Porrati (DGP) brane model is confronted by current cosmic observational data sets from geometrical and dynamical perspectives. On the geometrical side, the recently released Union2 557 of type Ia supernovae (SN Ia), the baryon acoustic oscillation from the Sloan Digital Sky Survey and the Two Degree Galaxy Redshift Survey (transverse and radial to line-of-sight data points), the cosmic microwave background measurement given by the seven-year Wilkinson Microwave Anisotropy Probe observations [shift parameters R, l(a)(z(*)) and redshift at the last scatter surface z(*)], ages of high redshifts galaxies, i.e., the lookback time and the high redshift gamma ray bursts are used. On the dynamical side, data points about the growth function of matter linear perturbations are used. Using the same data set combination, we also constrain the flat Lambda CDM model as a comparison. The results show that current geometrical and dynamical observational data sets much favor the flat Lambda CDM model and the departure from it is above 4 sigma(6 sigma) for the spatially flat DGP model with (without) SN systematic errors. The consistence of growth function data points is checked in terms of a relative departure of redshift-distance relation.