The star formation rate density and dust attenuation evolution over 12 Gyr with the VVDS surveys

International audience; We investigate the cosmic star formation rate density (SFRD) over ∼12 Gyr (0.05≤ z≤ 4.5), combining the VVDS Deep (17.5 ≤ I_{AB}≤ 24.0) and Ultra-Deep (23.00 ≤ i'_{AB} ≤ 24.75) surveys. We obtain a single homogeneous spectroscopic redshift sample, totalizing about 11000 galaxies. We estimate the rest-frame FUV luminosity function (LF) and luminosity density (LD), extract the dust attenuation of the FUV radiation using SED fitting, and derive the dust-corrected SFRD. We find a constant and flat faint-end slope alpha in the FUV LF at z2 it is on average brighter than in the literature, while φ^{*} is smaller. Our total LD shows a robust peak at z≃2, and the SFRD history peaks as well at z≃2. This peak is produced by the decreasing contribution at z2 the SFRD is entirely shaped by the high specific SFR galaxies. The presence of a fast rise at z>2 and of a clear peak at z≃2 of the SFRD is compelling for models of galaxy formation. The mean dust attenuation A_{FUV} of the global galaxy population rises by 1 mag from z=4.5 to z=2, reaches its maximum at z=1 (A_{FUV}≃2.2 mag), and then decreases by 1.1 mag down to z=0. The dust attenuation maximum is reached 2 Gyr after the SFRD peak, implying a contribution from the intermediate-mass stars to the dust production at z