  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.
