Does accelerating universe indicates Brans-Dicke theory

The evolution of universe in Brans-Dicke (BD) theory is discussed in this paper. Considering a parameterized scenario for BD scalar field $\phi=\phi_{0}a^{\alpha}$ which plays the role of gravitational "constant" $G$, we apply the Markov Chain Monte Carlo method to investigate a global constraints on BD theory with a self-interacting potential according to the current observational data: Union2 dataset of type supernovae Ia (SNIa), high-redshift Gamma-Ray Bursts (GRBs) data, observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. It is shown that an expanded universe from deceleration to acceleration is given in this theory, and the constraint results of dimensionless matter density $\Omega_{0m}$ and parameter $\alpha$ are, $\Omega_{0m}=0.286^{+0.037+0.050}_{-0.039-0.047}$ and $\alpha=0.0046^{+0.0149+0.0171}_{-0.0171-0.0206}$ which is consistent with the result of current experiment exploration, $\mid\alpha\mid \leq 0.132124$. In addition, we use the geometrical diagnostic method, jerk parameter $j$, to distinguish the BD theory and cosmological constant model in Einstein's theory of general relativity.Comment: 16 pages, 3 figure