Constraining Feeble Neutrino Interactions with Ultralight Dark Matter

If ultralight $(\ll$ eV), bosonic dark matter couples to right handed neutrinos, active neutrino masses and mixing angles depend on the ambient dark matter density. When the neutrino Majorana mass, induced by the dark matter background, is small compared to the Dirac mass, neutrinos are "pseudo-Dirac" fermions that undergo oscillations between nearly degenerate active and sterile states. We present a complete cosmological history for such a scenario and find severe limits from a variety of terrestrial and cosmological observables. For scalar masses in the "fuzzy" dark matter regime ($\sim 10^{-20}$ eV), these limits exclude couplings of order $10^{-30}$, corresponding to Yukawa interactions comparable to the gravitational force between neutrinos and surpassing equivalent limits on time variation in scalar-induced electron and proton couplings.