Non-Gaussianity of the cosmic infrared background anisotropies - II. Predictions of the bispectrum and constraints forecast

Using a full analytical computation of the bispectrum based on the halo model together with the halo occupation number, we derive the bispectrum of the cosmic infrared background (CIB) anisotropies that trace the clustering of dusty-star-forming galaxies. We focus our analysis on wavelengths in the far-infrared and the sub-millimeter typical of the Planck/HFI and Herschel/SPIRE instruments, 350, 550, 850 and 1380 mu m. We explore the bispectrum behaviour as a function of several models of evolution of galaxies and show that it is strongly sensitive to that ingredient. Contrary to the power spectrum, the bispectrum, at the four wavelengths, seems dominated by low-redshift galaxies. Such a contribution can be hardly limited by applying low flux cuts. We also discuss the contributions of halo mass as a function of the redshift and the wavelength, recovering that each term is sensitive to a different mass range. Furthermore, we show that the CIB bispectrum is a strong contaminant of the cosmic microwave background bispectrum at 850 mu m and higher. Finally, a Fisher analysis of the power spectrum, bispectrum alone and of the combination of both shows that degeneracies on the halo occupation distribution parameters are broken by including the bispectrum information, leading to tight constraints even when including foreground residuals.