We study the luminosity function of the high-redshift galaxy population with redshifts 3 \leq z \leq 4 Â using a purely I -band magnitude-selected spectroscopic sample obtained in the framework of the VIMOS VLT Deep Survey ( VVDS ) .
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 .
We find that in the redshift range 3 \leq z \leq 4 , the VVDS luminosity function is parameterized by \phi ^ { * } = 1.24 ^ { +0.48 } _ { -0.50 } 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 Ã Â { \cal L } _ { 1700 } ( M < -18.5 ) = 2.4 10 ^ { 19 } W Mpc ^ { -3 } and { \cal L } _ { 1700 } ^ { \mathrm { Total } } = 3.1 10 ^ { 19 } W Mpc ^ { -3 } , comparable to that estimated in other studies .
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 .