Effect of a Degenerate Neutrino Sea on Electromagnetism

Modern cosmological theories imply the existence of a universal degenerate Fermi sea of neutrinos. The fact that the Fermi energy $K_F$ varies from theory to theory could, in principle, be used to help decide which universe we live in. We show that a parity-violating term is introduced into Maxwell's equations as a result of the neutrino sea. In particular, we study whether a new, meaningful limit on the Fermi energy can be established by studying the propagation of light and the character of magnetic fields in such a neutrino sea. Unfortunately, the solutions to these equations show that the effect of the neutrino sea on electromagnetism is too small to be observed.