Capturing Non-Gaussianity of the Large-Scale Structure with Weighted Skew-Spectra

TL;DR

This paper demonstrates that weighted skew-spectra can effectively capture the non-Gaussian information of the large-scale structure, providing a computationally efficient alternative to the bispectrum for key cosmological parameters.

Contribution

It introduces weighted skew-spectra as a proxy for the bispectrum and shows they contain equivalent information for certain parameters, with detailed covariance analysis.

Findings

Weighted skew-spectra match bispectrum information for bias and non-Gaussianity parameters.

Full covariance matrix is essential for accurate parameter constraints.

Analysis covers local, equilateral, and spin-2 primordial bispectrum shapes.

Abstract

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.