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Constraints on the Brans-Dicke gravity theory with the Planck data

Based on the new cosmic CMB temperature data from the Planck satellite, the 9 year polarization data from the WMAP, the BAO distance ratio data from the SDSS and 6dF surveys, we place a new constraint on the Brans-Dicke theory. We adopt a parametrization $ζ=\ln(1+1/ω})$, where the general relativity (GR) limit corresponds to $ζ= 0$. We find no evidence of deviation from general relativity. At 95% probability, $-0.00246 < ζ< 0.00567$, correspondingly, the region $-407.0 < ω<175.87$ is excluded. If we restrict ourselves to the $ζ>0$ (i.e. $ω>0$) case, then the 95% probability interval is $ζ<0.00549$, corresponding to $ω> 181.65$. We can also translate this result to a constraint on the variation of gravitational constant, and find the variation rate today as $\dot{G}=-1.42^{+2.48}_{-2.27} \times 10^{-13} $yr$^{-1} $ ($1σ$ error bar), the integrated change since the epoch of recombination is $δG/G = 0.0104^{+0.0186}_{-0.0067} $ ($1σ$ error bar). These limits on the variation of gravitational constant are comparable with the precision of solar system experiments.