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We study the evolution of the star formation rate (SFR) – stellar mass (M⋆) relation and specific star formation rate (sSFR) of star-forming galaxies (SFGs) since a redshift z ≃ 5.5 using 2435 (4531) galaxies with highly reliable spectroscopic redshifts in the VIMOS Ultra-Deep Survey (VUDS). It is the first time that these relations can be followed over such a large redshift range from a single homogeneously selected sample of galaxies with spectroscopic redshifts. The log (SFR) − log (M⋆) relation for SFGs remains roughly linear all the way up to z = 5, but the SFR steadily increases at fixed mass with increasing redshift. We find that for stellar masses M⋆ ≥ 3.2 × 109M⊙ the SFR increases by a factor of ~13 between z = 0.4 and z = 2.3. Weextend this relation up to z = 5, finding an additional increase in SFR by a factor of 1.7 from z = 2.3 to z = 4.8 for masses M⋆ ≥ 1010M⊙. We observe a turn-off in the SFR–M⋆ relation at the highest mass end up to a redshift z ~ 3.5. We interpret this turn-off as the signature of a strong on-going quenching mechanism and rapid mass growth. The sSFR increases strongly up to z ~ 2, but it grows much less rapidly in 2 <z< 5. We find that the shape of the sSFR evolution is not well reproduced by cold gas accretion-driven models or the latest hydrodynamical models. Below z ~ 2 these models have a flatter evolution (1 + z)Φ with Φ = 2 − 2.25 compared to the data which evolves more rapidly with Φ = 2.8 ± 0.2. Above z ~ 2, the reverse is happening with the data evolving more slowly with Φ = 1.2 ± 0.1. The observed sSFR evolution over a large redshift range 0 <z< 5 and our finding of a non-linear main sequence at high mass both indicate that the evolution of SFR and M⋆ is not solely driven by gas accretion. The results presented in this paper emphasize the need to invoke a more complex mix of physical processes including major and minor merging to further understand the co-evolution of the SFR and stellar mass growth.
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