Non-Gaussianity of the Cosmic Infrared Background anisotropies I : Diagrammatic formalism and application to the angular bispectrum

We present the first halo model based description of the Cosmic Infrared Background (CIB) non-Gaussianity (NG) that is fully parametric. To this end, we introduce, for the first time, a diagrammatic method to compute high order polyspectra of the 3D galaxy density field. It allows an easy derivation and visualisation of the different terms of the polyspectrum. We apply this framework to the power spectrum and bispectrum, and we show how to project them on the celestial sphere in the purpose of the application to the CIB angular anisotropies. Furthermore, we show how to take into account the particular case of the shot noise terms in that framework. Eventually, we compute the CIB angular bispectrum at 857 GHz and study its scale and configuration dependencies, as well as its variations with the halo occupation distribution parameters. Compared to a previously proposed empirical prescription, such physically motivated model is required to describe fully the CIB anisotropies bispectrum. Finally, we compare the CIB bispectrum with the bispectra of other signals potentially present at microwave frequencies, which hints that detection of CIB NG should be possible above 220 GHz.