Planck intermediate results. XLI. A map of lensing-induced B-modes
  The secondary cosmic microwave background (CMB) $B$-modes stem from the
post-decoupling distortion of the polarization $E$-modes due to the
gravitational lensing effect of large-scale structures. These lensing-induced
$B$-modes constitute both a valuable probe of the dark matter distribution and
an important contaminant for the extraction of the primary CMB $B$-modes from
inflation. Planck provides accurate nearly all-sky measurements of both the
polarization $E$-modes and the integrated mass distribution via the
reconstruction of the CMB lensing potential. By combining these two data
products, we have produced an all-sky template map of the lensing-induced
$B$-modes using a real-space algorithm that minimizes the impact of sky masks.
The cross-correlation of this template with an observed (primordial and
secondary) $B$-mode map can be used to measure the lensing $B$-mode power
spectrum at multipoles up to $2000$. In particular, when cross-correlating with
the $B$-mode contribution directly derived from the Planck polarization maps,
we obtain lensing-induced $B$-mode power spectrum measurement at a significance
level of $12\,\sigma$, which agrees with the theoretical expectation derived
from the Planck best-fit $\Lambda$CDM model. This unique nearly all-sky
secondary $B$-mode template, which includes the lensing-induced information
from intermediate to small ($10\lesssim \ell\lesssim 1000$) angular scales, is
delivered as part of the Planck 2015 public data release. It will be
particularly useful for experiments searching for primordial $B$-modes, such as
BICEP2/Keck Array or LiteBIRD, since it will enable an estimate to be made of
the lensing-induced contribution to the measured total CMB $B$-modes.
