Using correlations between CMB lensing and large-scale structure to
  measure primordial non-Gaussianity
  We apply a new method to measure primordial non-Gaussianity, using the
cross-correlation between galaxy surveys and the CMB lensing signal to measure
galaxy bias on very large scales, where local-type primordial non-Gaussianity
predicts a $k^2$ divergence. We use the CMB lensing map recently published by
the Planck collaboration, and measure its external correlations with a suite of
six galaxy catalogues spanning a broad redshift range. We then consistently
combine correlation functions to extend the recent analysis by Giannantonio et
al. (2013), where the density-density and the density-CMB temperature
correlations were used. Due to the intrinsic noise of the Planck lensing map,
which affects the largest scales most severely, we find that the constraints on
the galaxy bias are similar to the constraints from density-CMB temperature
correlations. Including lensing constraints only improves the previous
statistical measurement errors marginally, and we obtain $ f_{\mathrm{NL}} = 12
\pm 21 $ (1$\sigma$) from the combined data set. However, the lensing
measurements serve as an excellent test of systematic errors: we now have three
methods to measure the large-scale, scale-dependent bias from a galaxy survey:
auto-correlation, and cross-correlation with both CMB temperature and lensing.
As the publicly available Planck lensing maps have had their largest-scale
modes at multipoles $l<10$ removed, which are the most sensitive to the
scale-dependent bias, we consider mock CMB lensing data covering all
multipoles. We find that, while the effect of $f_{\mathrm{NL}}$ indeed
increases significantly on the largest scales, so do the contributions of both
cosmic variance and the intrinsic lensing noise, so that the improvement is
small.
