Cumulative [CII] luminosity functions predicted at z ≃ 4 and z ≃ 6 (thick continuous blue and orange lines, respectively, with the thin lines representing ), compared to the current observational constraints (data points with error bars). The dot-dashed lines are derived by relaxing the criterium r_eq<r_g which concerns only <0.8% of the galaxies. The dashed lines show the [CII] luminosity functions derived from the carbon mass function of our model.