  We aim at finding a cosmologically motivated infall law to understand if the
LambdaCDM cosmology can reproduce the main chemical characteristics of a Milky
Way-like spiral galaxy. 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 LambdaCDM 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. The cosmological gas infall law predicts two
main gas accretion episodes. 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. 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.
