Cosmic neutrino background on the surface of the Earth

Abstract

We argue that the reflection of relic neutrinos from the surface of the Earth results in a significant local ν-ν¯ asymmetry, far exceeding the expected primordial lepton asymmetry. The net fractional electron neutrino number nνe-nν¯enνe is up to O(105)mν0.1 eV larger than that implied by the baryon asymmetry. This enhancement is due to the weak 4-Fermi repulsion of the νe from ordinary matter which slows down the νe near the Earth's surface, and to the resulting evanescent neutrino wave that penetrates below the surface. This repulsion thus creates a net νe overdensity in a shell ∼7 meters0.1 eVmν thick around the Earth's surface. Similarly the repulsion between ν¯μ or ν¯τ and ordinary matter creates an overdensity of ν¯μ,τ of similar size. These local enhancements increase the size of O(GF) torques of the CνB on spin-polarized matter by a factor of order 105. In addition, they create a gradient of the net neutrino density which naturally provides a way out of the forty-year-old "no-go"theorems on the vanishing of O(GF) forces. The torque resulting from such a gradient force can be 108 times larger than that of earlier proposals. Although the size of these effects is still far from current reach, they may point to new directions for CνB detection.