Evolution of Primordial Neutrino Helicities in Cosmic Gravitational Inhomogeneities

Relic neutrinos from the Big Bang decoupled from the hot plasma predominantly in helicity eigenstates. Their subsequent propagation through gravitational inhomogeneities of the Universe alters the helicities of both Dirac and Majorana neutrinos, thus providing an independent probe of the evolving universe. We determine here the probability that relic neutrinos flip their helicity, in terms of the spectrum of density inhomogeneities measured in the Cosmic Microwave Background. As we find, for Dirac neutrinos the gravitational helicity modifications are intermediate between the effects of magnetic fields if the neutrino magnetic moment is of the magnitude predicted in the Standard Model and the much larger effects if the magnetic moment is of the scale consistent with the excess of low energy electron events seen by the XENON1T experiment. We give succinct derivations, within general relativity, of the semi-classical response of a spinning particle to a weak gravitational field in an expanding universe, and estimate the helicity modifications of neutrinos emitted by the Sun caused by the Sun's gravity.