What Can We Learn by Combining the Skew Spectrum and the Power Spectrum?

Abstract: Clustering of the large scale structure provides complementary information to the measurements of the cosmic microwave background anisotropies through power spectrum and bispectrum of density perturbations. Extracting the bispectrum information, however, is more challenging than it is from the power spectrum due to the complex models and the computational cost to measure the signal and its covariance. To overcome these problems, we adopt a proxy statistic, skew spectrum which is a cross-spectrum of the density field and its quadratic field. By applying a large smoothing filter to the density field, we show the theory fits the simulations very well. With the spectra and their full covariance estimated from $N$-body simulations as our "mock" Universe, we perform a global fits for the cosmological parameters. The results show that adding skew spectrum to power spectrum the $1\sigma$ marginalized errors for parameters $ b_1^2A_s, n_s$ and $f_{\rm NL}^{\rm loc}$ are reduced by $31\%, 22\%, 44\%$, respectively. This is the answer to the question posed in the title and indicates that the skew spectrum will be a fast and effective method to access complementary information to that enclosed in the power spectrum measurements, especially for the forthcoming generation of wide-field galaxy surveys.