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 cos-
mic 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 um. 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 um and higher.
Finally, a Fisher analysis of the power spectrum, bispectrum alone and of the
combination of both shows that degeneracies on the HOD parameters are broken by
including the bispectrum information, leading to tight constraints even when
including foreground residuals.
