Halo/galaxy bispectrum with equilateral-type primordial trispectrum

We investigate the effect of equilateral-type primordial trispectrum on the halo/galaxy bispectrum. We consider three types of equilateral primordial trispectra which are generated by quartic operators naturally appearing in the effective field theory of inflation and can be characterized by three nonlinearity parameters, gNLσ4, gNLσ2(∂σ)2, and gNL(∂σ)4. Recently, constraints on these parameters have been investigated from Cosmic Microwave Background (CMB) observations by using WMAP9 data. In order to consider the halo/galaxy bispectrum with the equilateral-type primordial trispectra, we adopt the integrated perturbation theory in which the effects of primordial non-Gaussianity are wholly encapsulated in the linear primordial polyspectrum for the evaluation of the biased polyspectrum. We show the shapes of the halo/galaxy bispectrum with the equilateral-type primordial trispectra and find that the primordial trispectrum characterized by gNLσ4 provides the same scale dependence as the gravity-induced halo/galaxy bispectrum. Hence, it would be difficult to obtain the constraint on gNLσ4 from the observations of the halo/galaxy bispectrum. On the other hand, the primordial trispectra characterized by gNLσ2(∂σ)2 and gNL(∂σ)4 provide the common scale dependence which is different from that of the gravity-induced halo/galaxy bispectrum on large scales. Hence, future observations of the halo/galaxy bispectrum would give constraints on the nonlinearity parameters, gNLσ2(∂σ)2 and gNL(∂σ)4 independently from CMB observations.