Galaxy mergers are thought to be one of the main mechanisms of the mass assembly of galaxies. Recently, many works have suggested a possible increase in the fraction of major mergers in the early Universe, reviving the debate on which processes (e.g., cold accretion, star formation, mergers) most contribute to the mass build-up of galaxies through cosmic time. To estimate the importance of major mergers in this context, we make use of the new data collected by the ALMA Large Program to INvestigate [CII] at Early times (ALPINE), which observed the [CII] 158 $mu$m emission line from a sample of 75 main-sequence star-forming galaxies at 4.4 < z < 5.9. We used, for the first time, the morpho-kinematic information provided by the [CII] emission to obtain the fraction of major mergers ($f_{MM}$) at z~5. By adopting different prescriptions for the merger timescales ($T_{MM}$), we converted this fraction into the merger rate per galaxy ($R_{MM}$) and per volume ($Gamma_{MM}$). We then combined our results with those at lower redshifts from the literature, computing the cosmic evolution of the merger fraction. This is described by a rapid increase from z~0 to higher redshifts, a peak at z~3, and a slow decrease towards earlier epochs. Depending on the timescale prescription used, this fraction translates into a merger rate ranging between ~0.1 and ~4.0 Gyr$^{-1}$ at z~5. Finally, we compare the specific star formation and star-formation rate density with the analogous quantities from major mergers. Our new ALPINE data reveal the presence of a significant merging activity in the early Universe. However, whether this population of mergers can provide a relevant contribution to the galaxy mass assembly at these redshifts and through the cosmic epochs is strongly dependent on the assumption of the merger timescale.
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