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The [CII] 158 micron line is one of the strongest IR emission lines, whichhas been shown to trace the star-formation rate (SFR) of galaxies in the nearbyUniverse and up to $z \sim 2$. Whether this is also the case at higher redshiftand in the early Universe remains debated. The ALPINE survey, which targeted118 star-forming galaxies at $4.4 < z< 5.9$, provides a new opportunity toexamine this question with the first statistical dataset. Using the ALPINE dataand earlier measurements from the literature we examine the relation betweenthe [CII] luminosity and the SFR over the entire redshift range from $z \sim4-8$. ALPINE galaxies, which are both detected in [CII] and dust continuum,show a good agreement with the local L([CII])-SFR relation. Galaxies undetectedin the continuum with ALMA are found to be over-luminous in [CII], when the UVSFR is used. After accounting for dust-obscured star formation, by an amountSFR(IR)$\approx$SFR(UV) on average, which results from two different stackingmethods and SED fitting, the ALPINE galaxies show an L([CII])-SFR relationcomparable to the local one. When [CII] non-detections are taken into account,the slope may be marginally steeper at high-z, although this is still somewhatuncertain. When compared in a homogeneous manner, the $z>6 $ [CII] measurements(detections and upper limits) do not behave very differently from the $z \sim4-6$ data. We find a weak dependence of L([CII])/SFR on the Lyman-alphaequivalent width. Finally, we find that the ratio L([CII])/LIR $\sim (1-3)\times 10^{-3}$ for the ALPINE sources, comparable to that of "normal" galaxiesat lower redshift. Our analysis, which includes the largest sample ($\sim 150$galaxies) of [CII] measurements at $z>4$ available so far, suggests no orlittle evolution of the L([CII])-SFR relation over the last 13 Gyr of cosmictime.

The ALPINE-ALMA [CII] survey. Little to no evolution in the [CII]-SFR relation over the last 13 Gyr