The Evolution of the Luminosity Function in Deep Fields: A Comparison with CDM Models

The galaxy Luminosity Function (LF) has been estimated in the rest frame B luminosity at 0<z<1.25 and at 1700 {\AA} for 2.5<z<4.5 from deep multicolor surveys in the HDF-N, HDF-S, NTT-DF. 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<= 1, although the model LF has a steeper average slope at the faint end; at z~3 such feature results in an overprediction of the number of faint (I_{AB}~ 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 treatement 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.