The dust polarization is parameterized as a power law form of the multipole l : D ^ { XX } _ { l } = A ^ { XX } l ( l + 1 ) l ^ { \alpha _ { XX } } / ( 2 \pi ) ( XX denotes BB or EE ) , where A ^ { XX } is its amplitude with the ratio A ^ { BB } / A ^ { EE } = 0.52 \pm 0.02 and \alpha _ { BB,EE } = -2.42 \pm 0.02 .
Extrapolating to 150 GHz from 353 GHz yields a value of D ^ { BB } _ { l = 80 } = ( 1.32 \pm 0.29 ) \times 10 ^ { -2 } \mu K ^ { 2 } ( and an additional uncertainty ( +0.28 , -0.24 ) \times 10 ^ { -2 } \mu K ^ { 2 } ) over the range 40 < l < 120 .
Based on these data , we report the tensor-to-scalar ratio r = A _ { t } / A _ { s } defined at k _ { 0 } = 0.05 \text { Mpc } ^ { -1 } by joining the BICEP2+ Planck 2013+WMAP9+BAO+HST and Planck HFI 353 GHz dust polarization and its implication to the detection of the primordial gravitational waves .
Considering the \Lambda CDM+ r model , we found r < 0.108 at 95 \% confidence level with \sigma _ { stat } = 0.29 and r < 0.129 at 95 \% confidence level with \sigma _ { stat + extr } = 0.29 + 0.28 .
The results imply no significant evidence for the primordial gravitational waves in 1 \sigma regions .
However the post probability distribution of r peaks at a small positive value .
And r moves to larger positive values when the extrapolation error bars are included .
This might imply a very weak signal of the primordial gravitational waves .
It also implies the crucial fact in calibrating the amplitude of the dust polarizations in detecting the primordial gravitational waves in the future .
When the running of the scalar spectral tilt is included , we found r < 0.079 at 95 \% confidence level with \sigma _ { stat } = 0.29 and r = 0.091 _ { -0.069 } ^ { +0.042 } at 95 \% confidence level with \sigma _ { stat + extr } = 0.29 + 0.28 .
The later one implies the detection of the primordial gravitational waves in 1 \sigma regions at the cost of decreasing the value of D ^ { BB } _ { l = 80 } to 0.67 _ { -0.25 } ^ { +0.25 } .