Capturing Non-Gaussianity of the Large-Scale Structure with Weighted
  Skew-Spectra
  The forthcoming generation of wide-field galaxy surveys will probe larger
volumes and galaxy densities, thus allowing for a much larger signal-to-noise
ratio for higher-order clustering statistics, in particular the galaxy
bispectrum. Extracting this information, however, is more challenging than
using the power spectrum due to more complex theoretical modeling, as well as
significant computational cost of evaluating the bispectrum signal and the
error budget. To overcome these challenges, several proxy statistics have been
proposed in the literature, which partially or fully capture the information in
the bispectrum, while being computationally less expensive than the bispectrum.
One such statistics are {\it weighted skew-spectra}, which are cross-spectra of
the density field and appropriately weighted quadratic fields. Using Fisher
forecasts, we show that the information in these skew-spectra is equivalent to
that in the bispectrum for parameters that appear as amplitudes in the
bispectrum model, such as galaxy bias parameters or the amplitude of primordial
non-Gaussianity. We consider three shapes of the primordial bispectrum: local,
equilateral and that due to massive particles with spin two during inflation.
To obtain constraints that match those from a measurement of the full
bispectrum, we find that it is crucial to account for the full covariance
matrix of the skew-spectra.
