Planck 2013 results. XVIII. Gravitational lensing-infrared background
  correlation
  The multi-frequency capability of the Planck satellite provides information
both on the integrated history of star formation (via the cosmic infrared
background, or CIB) and on the distribution of dark matter (via the lensing
effect on the cosmic microwave background, or CMB). The conjunction of these
two unique probes allows us to measure directly the connection between dark and
luminous matter in the high redshift (1 < z <3) Universe. We use a three-point
statistic optimized to detect the correlation between these two tracers.
Following a thorough discussion of possible contaminants and a suite of
consistency tests, using lens reconstructions at 100, 143 and 217 GHz and CIB
measurements at 100-857 GHz, we report the first detection of the correlation
between the CIB and CMB lensing. The well matched redshift distribution of
these two signals leads to a detection significance with a peak value of 42
\sigma at 545 GHz and a correlation as high as 80% across these two tracers.
Our full set of multi-frequency measurements (both CIB auto- and CIB-lensing
cross-spectra) are consistent with a simple halo-based model, with a
characteristic mass scale for the halos hosting CIB sources of
log_{10}(M/M_sun) = 10.5 \pm 0.6. Leveraging the frequency dependence of our
signal, we isolate the high redshift contribution to the CIB, and constrain the
star formation rate (SFR) density at z>1. We measure directly the SFR density
with around 2 sigma significance for three redshift bins between z=1 and 7,
thus opening a new window into the study of the formation of stars at early
times.
