A joint analysis of Planck and BICEP2 B modes including dust
  polarization uncertainty
  We analyze BICEP2 and Planck data using a model that includes CMB lensing,
gravity waves, and polarized dust. Planck dust polarization maps have
highlighted the difficulty of estimating the 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 $C_{l}^{BB} \propto l^{-2.42}$.
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 HI column density and Planck
polarization measurements at 353 GHz in the BICEP2 field. Including the latter
constraint in our analysis improves the limit further to $r < 0.09$, placing
strong constraints on 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 $r<0.05$, 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. (Abridged.)
