We test several gas infall laws, starting from that suggested in the two-infall model for the chemical evolution of the Milky Way, but focusing on laws derived from cosmological simulations which follows a concordance $Lambda$CDM cosmology. By means of a detailed chemical evolution model we study the effects of the different gas infall laws on the abundance patterns and the G-dwarf metallicity distribution. One cosmological gas infall law in particular resembles the infall law suggested by the two-infall model. It predicts two main gas accretion episodes. Minor infall episodes are predicted to have followed the second main one but they are of little significance compared to the previous two. By means of this cosmologically motivated infall law, we study the star formation rate, the SNIa and SNII rate, the total amount of gas and stars and the behavior of several chemical abundances. We find that the results of the two-infall model are fully compatible with the evolution of the Milky Way with cosmological accretion laws.
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