We present infrared luminosity functions and dust mass functions for the EAGLE cosmological simulation, based on synthetic multi-wavelength observations generated with the SKIRT radiative transfer code. In the local Universe, we reproduce the observed infrared luminosity and dust mass functions very well. Some minor discrepancies are encountered, mainly in the high luminosity regime, where the EAGLE-SKIRT luminosity functions mildly but systematically underestimate the observed ones. The agreement between the EAGLE-SKIRT infrared luminosity functions and the observed ones gradually worsens with increasing lookback time. Fitting modified Schechter functions to the EAGLE-SKIRT luminosity and dust mass functions at different redshifts up to $z=1$, we find that the evolution is compatible with pure luminosity/mass evolution. The evolution is relatively mild: within this redshift range, we find an evolution of $L_{star,250}propto(1+z)^{1.68}$, $L_{star,text{TIR}}propto(1+z)^{2.51}$ and $M_{star,text{dust}}propto(1+z)^{0.83}$ for the characteristic luminosity/mass. For the luminosity/mass density we find $varepsilon_{250}propto(1+z)^{1.62}$, $varepsilon_{text{TIR}}propto(1+z)^{2.35}$ and $rho_{text{dust}}propto(1+z)^{0.80}$, respectively. The mild evolution of the dust mass density is in relatively good agreement with observations, but the slow evolution of the infrared luminosity underestimates the observed luminosity evolution significantly. We argue that these differences can be attributed to increasing limitations in the radiative transfer treatment due to increasingly poorer resolution, combined with a slower than observed evolution of the SFR density in the EAGLE simulation and the lack of AGN emission in our EAGLE-SKIRT post-processing recipe.
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