Isotropic diffuse and extragalactic $\gamma$-ray background: emission from extragalactic sources vs dark matter annihilating particles

The isotropic diffuse $\gamma$-ray background (IGRB) has been detected by various experiments and recently the Fermi-LAT Collaboration has precisely measured its spectrum in a wide energy range. The origin of the IGRB is still unclear and we show in this paper the significative improvements that have been done, thanks to the new Fermi-LAT catalogs, to solve this mystery. We demonstrate that the $\gamma$-ray intensity and spectrum of the IGRB is fully consistent with the unresolved emission from extragalactic point sources, namely Active Galactic Nuclei and Star Forming Galaxies. We show also that the IGRB can be employed to derive sever constraints for the $\gamma$-ray emission from diffuse processes such as annihilation of Dark Matter (DM) particles. Our method is able to provide low bounds for the thermal annihilation cross section for a wide range of DM masses.