The cosmic spectral energy distribution (CSED) is the total emissivity as a function of wavelength of galaxies in a given cosmic volume. We compare the observed CSED from the UV to the submm to that computed from the EAGLE cosmological hydrodynamical simulation, post-processed with stellar population synthesis models and including dust radiative transfer using the SKIRT code. The agreement with the data is better than 0.15 dex over the entire wavelength range at redshift $z=0$, except at UV wavelengths where the EAGLE model overestimates the observed CSED by up to a factor 2. Global properties of the CSED as inferred from CIGALE fits, such as the stellar mass density, mean star formation density, and mean dust-to-stellar-mass ratio, agree to within better than 20 per cent. At higher redshift, EAGLE increasingly underestimates the CSED at optical-NIR wavelengths with the FIR/submm emissivity underestimated by more than a factor of 5 by redshift $z=1$. We believe that these differences are due to a combination of incompleteness of the EAGLE-SKIRT database, the small simulation volume and the consequent lack of luminous galaxies, and our lack of knowledge on the evolution of the characteristics of the interstellar dust in galaxies. The impressive agreement between the simulated and observed CSED at lower $z$ confirms that the combination of EAGLE and SKIRT dust processing yields a fairly realistic representation of the local Universe.
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