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

Abstract

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+(1)/(ω)), 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^-13yr^-1 (1σ error bar); the integrated change since the epoch of recombination is δG/G=0.0104_-0.0067^+0.0186 (1σ error bar). These limits on the variation of the gravitational constant are comparable with the precision of Solar System experiments.