We study the evolution of the star formation rate ( SFR ) – stellar mass ( M _ { \star } ) relation and specific star formation rate ( sSFR ) of star forming galaxies ( SFGs ) since a redshift z \simeq 5.5 using 2435 ( 4531 ) galaxies with highly reliable ( 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 _ { \star } ) 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 _ { \star } \geq 3.2 \times 10 ^ { 9 } M _ { \sun } the SFR increases by a factor \sim 13 between z = 0.4 and z = 2.3 .
We extend this relation up to z = 5 , finding an additional increase in SFR by a factor 1.7 from z = 2.3 to z = 4.8 for masses M _ { \star } \geq 10 ^ { 10 } M _ { \sun } .
We observe a turn–off in the SFR–M _ { \star } relation at the highest mass end up to a redshift z \sim 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 \sim 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 \sim 2 these models have a flatter evolution ( 1 + z ) ^ { \Phi } with \Phi = 2 - 2.25 compared to the data which evolves more rapidly with \Phi = 2.8 \pm 0.2 .
Above z \sim 2 , the reverse is happening with the data evolving more slowly with \Phi = 1.2 \pm 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 _ { \star } 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 star formation rate and stellar mass growth .