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

Aims. We investigate the global galaxy evolution over similar to 12 Gyr (0.05 <= z <= 4.5), from the far ultraviolet (FUV) luminosity function (LF), luminosity density (LD), and star formation rate density (SFRD), using the VIMOS-VLT Deep Survey (VVDS), a single deep galaxy redshift survey with a well controlled selection function. Methods. We combine the VVDS Deep (17.5 <= I-AB <= 24.0) and Ultra-Deep (23.00 <= i'(AB) = 24.75) redshift surveys, totalizing similar to 11 000 galaxies, to estimate the rest-frame FUV LF and LD, using a wide wavelength range of deep photometry (337 < lambda < 2310 nm). We extract the dust attenuation of the FUV radiation, embedded in the well-constrained spectral energy distributions. We then derive the dust-corrected SFRD. Results. We find a constant and flat faint-end slope a in the FUV LF at z < 1.7. At z > 1.7, we set a steepening with (1+ z). The absolute magnitude M* FUV steadily brightens in the entire range 0 < z < 4.5, and at z > 2 it is on average brighter than in the literature, while phi* is on average smaller. The evolution of our total LD shows a peak at z similar or equal to 2, clearly present also when considering all sources of uncertainty. The SFRD history peaks as well at z similar or equal to 2. It first steadily rises by a factor of similar to 6 during 2 Gyr (from z = 4.5 to z = 2), and then decreases by a factor of similar to 12 during 10 Gyr down to z = 0.05. This peak is mainly produced by a similar peak within the population of galaxies with -21.5 = MFUV = -19.5. As times goes by, the total SFRD is dominated by fainter and fainter galaxies. The mean dust attenuation of the global galaxy population rises fast by 1 mag during 2 Gyr from z similar or equal to 4.5 to z similar or equal to 2, reaches slowly its maximum at z similar or equal to 1 (A(FUV) similar or equal to 2.2 mag), and then decreases by 1.1 mag during 7 Gyr down to z similar or equal to 0. Conclusions. We have derived the cosmic SFRD history and the total dust amount in galaxies over a continuous period of similar to 12 Gyr, using a single homogeneous spectroscopic redshift sample. The presence of a clear peak at z similar or equal to 2 and a fast rise at z > 2 of the SFRD is compelling for models of galaxy formation. This peak is mainly produced by bright galaxies (L >= L*(z = 2)), requiring that significant gas reservoirs still exist at this epoch and are probably replenished by cold accretion and wet mergers, while feedback or quenching processes are not yet strong enough to lower the SF. The dust attenuation maximum is reached similar to 2 Gyr after the SFRD peak, implying a contribution from the intermediate-mass stars to the dust production at z < 2.