The VIMOS VLT deep survey - The ultraviolet galaxy luminosity function and luminosity density at 3 <= z <= 4

Aims. We study the luminosity function of the high-redshift galaxy population with redshifts 3 <= z <= 4 using a purely I-band magnitude-selected spectroscopic sample obtained in the framework of the VIMOS VLT Deep Survey (VVDS). Methods. We determine the luminosity function from the VVDS, taking care to add as few assumptions and as simple corrections as possible, and compare our results with those obtained from photometric studies, based on Lyman-break selections or photometric-redshift measurements. Results. We find that in the redshift range 3 <= z <= 4, the VVDS luminosity function is parameterized by phi* = 1.24(-0.50)(+0.48) x 10(-3) mag(-1) Mpc(-3) and M* = -21.49(-0.19)(+0.19), assuming a slope alpha = -1.4 consistent with most previous studies. While phi* is comparable to previously found values, M* is significantly brighter by about 0.5 mag at least. Using the conservative slope alpha = -1.4, we find a luminosity density at 1700 angstrom L-1700 (M < -18.5) = 2.4 x 10(19) W Mpc(-3) and L-1700(Total) = 3.1 x 10(19) W Mpc(-3), comparable to that estimated in other studies. Conclusions. The unexpectedly large number of very bright galaxies found in the VVDS indicates that the color-selection and photometric-redshift techniques that are generally used to build high-redshift galaxy samples may be affected by a significant fraction of color-measurement failures or by incomplete modelling of the mix of stellar emission, AGN contribution, dust absorption and intergalactic extinction assumed to identify high-redshift galaxies, making pure magnitude selection better able to trace the full population. Because of the difficulty to identify all low-luminosity galaxies in a spectroscopic survey, the luminosity density could still be significantly underestimated. We also find that the relative contribution of the most luminous galaxies compared to the fainter ones is at least twice as large in the VVDS compared to former estimates. Therefore, the VVDS paints a quite different picture of the role of the most actively star-forming galaxies in the history of star formation