Primordial non-Gaussianity in the bispectra of large-scale structure
The statistics of large-scale structure in the Universe can be used to probe non-Gaussianity of the primordial density field, complementary to existing constraints from the cosmic microwave background. In particular, the scale dependence of halo bias, which affects the halo distribution at large scales, represents a promising tool for analyzing primordial non-Gaussianity of local form. Future observations, for example, may be able to constrain the trispectrum parameter g{sub NL} that is difficult to study and constrain using the CMB alone. We investigate how galaxy and matter bispectra can distinguish between the two non-Gaussian parameters f{sub NL} and g{sub NL}, whose effects give nearly degenerate contributions to the power spectra. We use a generalization of the univariate bias approach, making the hypothesis that the number density of halos forming at a given position is a function of the local matter density contrast and of its local higher-order statistics. Using this approach, we calculate the halo-matter bispectra and analyze their properties. We determine a connection between the sign of the halo bispectrum on large scales and the parameter g{sub NL}. We also construct a combination of halo and matter bispectra that is sensitive to f{sub NL}, with little contamination from g{sub NL}. We study both the case of single and multiple sources to the primordial gravitational potential, discussing how to extend the concept of stochastic halo bias to the case of bispectra. We use a specific halo mass-function to calculate numerically the bispectra in appropriate squeezed limits, confirming our theoretical findings.