Using the covariant formalism developed in a companion paper [F.-Q. Wu, L. E. Qiang, X. Wang, and X. Chen, preceding Article, Phys. Rev. D 82, 083002 (2010)] (paper I), we derive observational constraints on the Brans-Dicke model in a flat Friedmann-Lemaître-Robertson-Walker universe with a cosmological constant and cold dark matter. The CMB observations we use include the Wilkinson Microwave Anisotropy Probe 5 yr data, the Arcminute Cosmology Bolometer Array Receiver 2007 data, the Cosmic Background Imager polarization data, and the Balloon Observations of Millimetric Extragalactic Radiation and Geophysics 2003 flight data. For the large scale structure we use the matter power spectrum data measured with the luminous red galaxy survey of the Sloan Digital Sky Survey Data Release 4. We parametrize the Brans-Dicke parameter $\omega$ with a new parameter $\zeta =\ln (1/\omega +1)$, and use the Markov-Chain Monte Carlo method to explore the parameter space. We find that using CMB data alone, one could place some constraints on positive $\zeta$ or $\omega$, but negative $\zeta$ or $\omega$ could not be constrained effectively. However, with additional large scale structure data, one could break the degeneracy at $\zeta <0$. The $2\sigma$ (95.5%) bound on $\zeta$ is $-0.00837<\zeta <0.01018$ (corresponding to $\omega <-120.0$ or $\omega >97.8$). We also obtained constraints on $\dot{G}/G$, the rate of change of $G$ at present, as $-1.75\times {10}^{-12}{\mathrm{yr}}^{-1}<\dot{G}/G<1.05\times {10}^{-12}{\mathrm{yr}}^{-1}$, and $\delta G/G$, the total variation of $G$ since the epoch of recombination, as $-0.083<\delta G/G<0.095$ at the $2\sigma$ confidence level.

• Received 23 December 2009

DOI:https://doi.org/10.1103/PhysRevD.82.083003