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

Based on the new cosmic microwave background temperature data from the Planck satellite, the nine-year polarization data from the Wilkinson Microwave Anisotropy Probe, and the baryon acoustic oscillation distance ratio data from the Sloan Digital Sky Survey and Six-Degree-Field surveys, we place a new constraint on the Brans-Dicke theory. We adopt a parametrization ζ=ln(1+1ω), where the general relativity 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 the gravitational constant and find the variation rate today as ${ ̇ {}}{G}={-}{1.42}_{{-}2.27}+2.48×{}{10}^{{-}13} {yr}^{{-}1}$ ($1{σ}$ error bar); the integrated change since the epoch of recombination is ${δ}G/G={0.0104}_{{-}0.0067}+0.0186$ ($1{σ}$ error bar). These limits on the variation of the gravitational constant are comparable with the precision of Solar System experiments.