Lithium Diffusion in the Post-Recombination Universe and Spatial Variation of [Li/H]

The observed amount of lithium for low metallicity population II stars (known as the Spite plateau) is a factor of $\sim 3-5$ lower than the predictions of the standard cosmology. Since the observations are limited to the local Universe (halo stars, globular clusters and satellites of the Milky Way) it is possible that certain physical processes may have led to the spatial separation of lithium and local reduction of [Li/H]. We study the question of lithium diffusion after the cosmological recombination in sub-Jeans dark matter haloes, taking into account that more than 95% of lithium remains in the singly-ionized state at all times. Large scattering cross sections on the rest of the ionized gas leads to strong coupling of lithium to protons and its initial direction of diffusion coincides with that of H$^+$. In the rest frame of the neutral gas this leads to the diffusion of H$^+$ and Li$^+$ out of overdensities with the trend of reducing [Li/H] in the minima of gravitational wells relative to the primordial value. We quantify this process and argue that, with certain qualifications, it may have played a significant role in creating local lithium deficiency within the primordial dark matter haloes, comparable to those observed along the Spite plateau.