The evolution of the galaxy luminosity function in the rest frame blue band up to z=3.5

We present an estimate of the cosmological evolution of the field galaxy luminosity function (LF) in the rest frame 4400 Angstrom B -band up to redshift z=3.5. To this purpose, we use a composite sample of 1541 I--selected galaxies selected down to I_(AB)=27.2 and 138 galaxies selected down to K_(AB)=25 from ground-based and HST multicolor surveys, most notably the new deep JHK images in the Hubble Deep Field South (HDF-S) taken with the ISAAC instrument at the ESO-VLT telescope. About 21% of the sample has spectroscopic redshifts, and the remaining fraction well calibrated photometric redshifts. The resulting blue LF shows little density evolution at the faint end with respect to the local values, while at the bright end (M_B(AB)<-20) a brightening increasing with redshift is apparent with respect to the local LF. Hierarchical CDM models overpredict the number of faint galaxies by about a factor 3 at z=1. At the bright end the predicted LFs are in reasonable agreement only at low and intermediate redshifts (z=1), but fail to reproduce the pronounced brightening observed in the high redshift (z=2-3) LF. This brightening could mark the epoch where a major star formation activity is present in the galaxy evolution.