Gas is a crucial component of galaxies, providing the fuel to form stars, and it is impossible to understand the evolution of galaxies without knowing their gas properties. The [CII] fine structure transition at 158 μm is the dominant cooling line of cool interstellar gas, and is the brightest of emission lines from star forming galaxies from FIR through metre wavelengths, almost unaffected by attenuation. 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 star formation rate (SFR) indicator at z ≥ 4. In this paper, we have used a semi-analytical model of galaxy evolution (G.A.S.) combined with the photoionisation code CLOUDY to predict the [CII] luminosity of a large number of galaxies (25 000 at z ≃ 5) at 4 ≤ z ≤ 8. We assumed that the [CII]-line emission originates from photo-dominated regions. At such high redshift, the CMB represents a strong background and we discuss its effects on the luminosity of the [CII] line. We studied the L[CII]–SFR and L[CII]–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 SFRs but the correlations are very broad, with a scatter of about 0.5 and 0.8 dex for L[CII]–SFR and L[CII]–Zg, respectively. Our model reproduces the L[CII]–SFR relations observed in high-redshift star-forming galaxies, with [CII] luminosities lower than expected from local L[CII]–SFR relations. Accordingly, the local observed L[CII]–SFR relation does not apply at high-z (z ≳ 5), even when CMB effects are ignored. Our model naturally produces the [CII] deficit (i.e. the decrease of L[CII]/LIR with LIR), 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 L[ CII] probed by the model (1 × 107–2 × 109 L⊙ at z = 6) with a slope α = −1. The slope is not evolving from z = 4 to z = 8 but the number density of [CII]-emitters decreases by a factor of 20×. We discuss our predictions in the context of current observational estimates on both the differential and cumulative luminosity functions
