  We aim at studying the effect of a cosmologically motivated gas infall law
for the formation of a massive elliptical galaxy in order to understand its
impact on the formation of the spheroids. We replace the empirical infall law
of the model by Pipino & Matteucci with a cosmologically derived infall law for
the formation of an elliptical galaxy. We constrast our predictions with
observations. We also compare the obtained results with those of Pipino &
Matteucci. We computed models with and without galactic winds: we found that
models without wind predict a too large current SNIa rate. In particular, the
cosmological model produces a current SNIa which is about ten times higher than
the observed values. Moreover models without wind predict a large current SNII
rate, too large even if compared with the recent GALEX data. The predicted SNII
rate for the model with wind, on the other hand, is too low if compared with
the star formation histories given by GALEX. Last but not least, the mean value
for the [Mg/Fe] ratio in the dominant stellar population of the simulated
galaxy, as predicted by the cosmological model, is too low if compared to
observations. This is, a very important result indicating that the cosmological
infall law is in contrast with the chemical evolution. A cosmologically derived
infall law for an elliptical galaxy cannot reproduce all the chemical
constraints given by the observations. The problem resides in the fact that the
cosmologically derived infall law implies a slow gas accretion with consequent
star formation rate active for a long period. In this situation low [Mg/Fe]
ratios are produced for the dominant stellar population in a typical
elliptical, at variance with observations.
