We analyze BICEP2 and Planck data using a model that includes CMB lensing , gravity waves , and polarized dust .
Recently published Planck dust polarization maps have highlighted the difficulty of estimating the amount of dust polarization in low intensity regions , suggesting that the polarization fractions have considerable uncertainties and may be significantly higher than previous predictions .
In this paper , we start by assuming nothing about the dust polarization except for the power spectrum shape , which we take to be C _ { l } ^ { BB, { dust } } \propto l ^ { -2.42 } .
The resulting joint BICEP2+Planck analysis favors solutions without gravity waves , and the upper limit on the tensor-to-scalar ratio is r < 0.11 , a slight improvement relative to the Planck analysis alone which gives r < 0.13 ( 95 % c.l . ) .
The estimated amplitude of the dust polarization power spectrum agrees with expectations for this field based on both H I column density and Planck polarization measurements at 353 GHz in the BICEP2 field .
Including the latter constraint on the dust spectrum amplitude in our analysis improves the limit further to r < 0.09 , placing strong constraints on theories of inflation ( e.g. , models with r > 0.14 are excluded with 99.5 % confidence ) .
We address the cross-correlation analysis of BICEP2 at 150 GHz with BICEP1 at 100 GHz as a test of foreground contamination .
We find that the null hypothesis of dust and lensing with r = 0 gives \Delta \chi ^ { 2 } < 2 relative to the hypothesis of no dust , so the frequency analysis does not strongly favor either model over the other .
We also discuss how more accurate dust polarization maps may improve our constraints .
If the dust polarization is measured perfectly , the limit can reach r < 0.05 ( or the corresponding detection significance if the observed dust signal plus the expected lensing signal is below the BICEP2 observations ) , but this degrades quickly to almost no improvement if the dust calibration error is 20 % or larger or if the dust maps are not processed through the BICEP2 pipeline , inducing sampling variance noise .