Based on the new cosmic microwave background ( CMB ) temperature data from the Planck satellite , the 9 year polarization data from the Wilkinson Microwave Anisotropy Probe ( WMAP ) , and the baryon acoustic oscillation ( BAO ) distance ratio data from the Sloan Digital Sky Survey ( SDSS ) and 6 Degree field ( 6dF ) surveys , we place a new constraint on the Brans-Dicke theory .
We adopt a parametrization \zeta = \ln ( 1 + \frac { 1 } { \omega } ) , where the general relativity ( GR ) limit corresponds to \zeta = 0 .
We find no evidence of deviation from general relativity .
At 95 % probability , -0.00246 < \zeta < 0.00567 , correspondingly , the region -407.0 < \omega < 175.87 is excluded .
If we restrict ourselves to the \zeta > 0 ( i.e . \omega > 0 ) case , then the 95 % probability interval is \zeta < 0.00549 , corresponding to \omega > 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 } ( 1 \sigma error bar ) , the integrated change since the epoch of recombination is \delta G / G = 0.0104 ^ { +0.0186 } _ { -0.0067 } ( 1 \sigma error bar ) .
These limits on the variation of gravitational constant are comparable with the precision of solar system experiments .