If neutrino masses are clocks, can we hear them tick?

Ultralight scalars are compelling candidates for dark matter. If they couple to neutrinos they induce a time dependent correction to their masses. In this talk we will discuss the consequences of this interaction covering a broad range of ultralight scalar masses. We will show how the time dependence, even if mild, could lead to a confusion of the neutrino mass ordering determination when combining data from long baseline neutrino experiments with JUNO. For that we will also show how neutrinos propagating through an ultralight scalar background can be mapped onto an open system approach of neutrino oscillations, providing a concrete mapping from model parameters (scalar mass and coupling) to the pure phenomenological constraints existing in the literature. Surprisingly, this very simple model leads to a scaling of the open system corrections with respect to the experiment baseline $L$ and neutrino energy $E$ different from what was previously explored in the literature, growing as $L^2/E^2$. We will comment how this framework may open new avenues to be explored in future work.