The Density of Relic Neutrinos Near the Surface of Earth

It has been claimed that matter effects cause an asymmetry in the density of relic neutrinos versus antineutrinos near the surface of Earth, of order $O(G_F^{1\mathrm{/}2})\sim {10}^{-4}$, with the vertical extent $\sim 10$m. We argue that the effect is of order $O(G_F)\sim {10}^{-8}$, with the vertical extent $\sim 1$mm.