Constraining higher-order parameters for primordial non-Gaussianities from power spectra and bispectra of imaging survey

We investigate the statistical power of higher-order statistics and cross-correlation statistics to constrain the primordial non-Gaussianity from the imaging surveys. In particular, we consider the local-type primordial non- Gaussianity and discuss how well one can tightly constrain the higher-order non-Gaussian parameters (\(g_{\rm NL}\) and \(\tau_{\rm NL}\)) as well as the leading order parameter \(f_{\rm NL}\) from the halo/galaxy clustering and weak gravitational lensing measurements. Making use of a strong scale-dependent behavior in the galaxy/halo clustering, Fisher matrix analysis reveals that the bispectra can break the degeneracy between non-Gaussian parameters (\(f_{\rm NL}\), \(g_{\rm NL}\) and \(\tau_{\rm NL}\)) and this will give simultaneous constraints on those three parameters. The combination of cross-correlation statistics further improves the constraints by factor of 2. As a result, upcoming imaging surveys like the Large Synoptic Survey Telescope have the potential to improve the constraints on the primordial non-Gaussianity much tighter than those obtained from the CMB measurement by Planck, giving us an opportunity to test the single-sourced consistency relation, \(\tau_{\rm NL} \ge (36/25) f_{\rm NL}^2\).