Probing scalar dark matter oscillations with neutrino oscillations

If ultra-light dark matter (ULDM) exists and couples to neutrinos, it can be discovered via time-periodic variations in the neutrino mass and mixing parameters. We analyze the current bounds on such a scenario and establish the sensitivity expected for both time-averaged and time-resolved modulations in future neutrino oscillation experiments. We place a special emphasis in our analysis on time modulations of the CP violating mixing phase. We illustrate with a toy model the case where the leading modulation effect can be CP violating while the effect on CP conserving parameters is suppressed. We show a unique imprint that a time-averaged CP violating modulation of ULDM can leave in neutrino oscillations, while direct CP asymmetries vanish.