Atomic diffusion in metal-poor stars. II. Predictions for the Spite plateau

We have computed a grid of up-to-date stellar evolutionary models including atomic diffusion, in order to study the evolution with time of the surface Li abundance in low-mass metal-poor stars. We discuss in detail the dependence of the surface Li evolution on the initial metallicity and stellar mass, and compare the abundances obtained from our models with the available Li measurements in Pop II stars. While it is widely accepted that the existence of the Spite Li-plateau for these stars is a strong evidence that diffusion is inhibited, we show that, when taking into account observational errors, uncertainties in the Li abundance determinations, in the T_eff scale, and in particular the size of the observed samples of stars, the Spite plateau and the Li abundances in subgiant branch stars can be reproduced also by models including fully efficient diffusion, provided that the most metal-poor field halo objects are between 13.5 and 14 Gyr old. We provide the value of the minimum number of plateau stars to observe, for discriminating between efficient or inhibited diffusion. {From} our models with diffusion we derive that the average Li abundance along the Spite plateau is about a factor of 2 lower than the primordial one. As a consequence, the derived primordial Li abundance would be consistent with a high helium and low deuterium Big Bang Nucleosynthesis; this implies a high cosmological baryon density as inferred from the analyses of the cosmic microwave background.