Cosmic rays from multi-wavelength observations of the Galactic diffuse emission

Cosmic rays (CRs) generate diffuse emission while interacting with the Galactic magnetic field (B-field), the interstellar gas and the radiation field. This diffuse emission extends from radio, microwaves, through X-rays, to high-energy gamma rays. Diffuse emission has considerably increased the interest of the astrophysical community due to recent detailed observations by Planck, Fermi-LAT, and by very-high energy Cherenkov telescopes. Observations of this diffuse emission and comparison with detailed predictions are used to gain information on the properties of CRs, such as their density, spectra, distribution and propagation in the Galaxy. Unfortunately disentangling and characterizing this diffuse emission strongly depends on uncertainties in the knowledge of unresolved sources, gas, radiation fields, and B-fields, other than CRs throughout the Galaxy. We discuss here the diffuse emission produced by CRs and its uncertainties, and the comparison of this predicted emission with recent multi-wavelength observations. We show insights on CR spectra and intensities. Then we address the importance for forthcoming telescopes, especially for the Square Kilometre Array telescope (SKA) and the Cherenkov Telescope Array (CTA), and for missions at MeV. (paper)