The evolution of the luminosity function in deep fields: A comparison with cold dark matter models

The galaxy luminosity function (LF) has been estimated in the rest-frame B luminosity at 0 < z < 1.25 and at 1700 Angstrom for 2.5 < z < 4.5 from deep multicolor surveys in the Hubble Deep Field-North, the Hubble Deep Field-South, and the New Technology Telescope Deep Field. The results have been compared with a recent version of galaxy formation models in the framework of hierarchical clustering in a flat cold dark matter universe with cosmological constant. The results show a general agreement for z less than or similar to 1, although the model LF has a steeper average slope at the faint end; at z similar to 3 such a feature results in an overprediction of the number of faint (I-AB similar to 27) galaxies, while the agreement at the bright end becomes critically sensitive to the details of dust absorption at such redshifts. The discrepancies at the faint end show that a refined treatment of the physical processes involving smaller galaxies is to be pursued in the models, in terms of aggregation processes and/or stellar feedback heavily affecting the luminosity of the low-luminosity objects. The implications of our results on the evolution of the cosmological star formation rate are discussed.