The [CII] fine structure transition at 158 microns is the dominant cooling line of cool interstellar gas, and is the brightest of emission lines from star forming galaxies from FIR through meter wavelengths. With the advent of ALMA and NOEMA, capable of detecting [CII]-line emission in high-redshift galaxies, there has been a growing interest in using the [CII] line as a probe of the physical conditions of the gas in galaxies, and as a SFR indicator at z>4. In this paper, we use a semi-analytical model of galaxy evolution (G.A.S.) combined with the code CLOUDY to predict the [CII] luminosity of a large number of galaxies at 4< z<8. At such high redshift, the CMB represents a strong background and we discuss its effects on the luminosity of the [CII] line. We study the LCII-SFR and LCII-Zg relations and show that they do not strongly evolve with redshift from z=4 and to z=8. Galaxies with higher [CII] luminosities tend to have higher metallicities and higher star formation rates but the correlations are very broad, with a scatter of about 0.5 dex for LCII-SFR. Our model reproduces the LCII-SFR relations observed in high-redshift star-forming galaxies, with [CII] luminosities lower than expected from local LCII-SFR relations. Accordingly, the local observed LCII-SFR relation does not apply at high-z. Our model naturally produces the [CII] deficit, which appears to be strongly correlated with the intensity of the radiation field in our simulated galaxies. We then predict the [CII] luminosity function, and show that it has a power law form in the range of LCII probed by the model with a slope alpha=1. The slope is not evolving from z=4 to z=8 but the number density of [CII]-emitters decreases by a factor of 20x. We discuss our predictions in the context of current observational estimates on both the differential and cumulative luminosity functions.
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