Does accelerating universe indicate Brans-Dicke theory?

The evolution of the universe in Brans-Dicke (BD) theory is discussed in this paper. Considering a parameterized scenario for BD scalar field φ = φ0aα 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: the Union2 dataset of type-Ia supernovae (SNIa), the high-redshift Gamma-Ray Bursts (GRBs) data, the 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 Ω0m and parameter α are, Ω0m = 0.286−0.039−0.047+0.037+0.050 and α = 0.0046−0.0171−0.0206+0.0149+0.0171 which is consistent with the result of current experiment exploration, |α| ≤ 0.132124. In addition, we use the geometrical diagnostic method, jerk parameter j, to distinguish the BD theory and the cosmological constant model in Einstein’s theory of general relativity.