Context :

Aims : We aim at finding a cosmologically motivated infall law to understand if the \Lambda CDM cosmology can reproduce the main chemical characteristics of a Milky Way-like spiral galaxy .

Methods : In this work we test several different gas infall laws , starting from that suggested in the two-infall model for the chemical evolution of the Milky Way by Chiappini et al. , but focusing on laws derived from cosmological simulations which follows a concordance \Lambda CDM cosmology .
By means of a detailed chemical evolution model for the solar vicinity , we study the effects of the different gas infall laws on the abundance patterns and the G-dwarf metallicity distribution .

Results : The cosmological gas infall law , derived from dark matter halos having properties compatible with the formation of a disk galaxy like the Milky Way , and assuming that the baryons assemble like dark matter , resembles the infall law suggested by the two-infall model .
In particular , it predicts two main gas accretion episodes .
Minor infall episodes are predicted to have followed the second main one but they are of small 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 in the solar neighbourhood and the behaviour 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 .
We derive that the timescale for the formation of the stellar halo and the thick disk must have not been longer than 2 Gyr , whereas the disk in the solar vicinity assembled on a much longer timescale ( \sim 6 Gyr ) .

Conclusions : A gas assembly history derived from a DM halo , compatible with the formation of a late-type galaxy from the morphological point of view , can produce chemical properties in agreement with the available observations .