  We investigate a consistent scenario of time-varying neutrino masses, and
discuss its impact on cosmology, beta decay, and neutrino oscillation
experiments. Such time-varying masses are assumed to be generated by the
coupling between a sterile neutrino and an ultralight scalar field, which in
turn affects the light neutrinos by mixing. Besides, the scalar could act as an
ultralight dark matter candidate. We demonstrate how various cosmological
bounds, such as those coming from Big Bang nucleosynthesis, the cosmic
microwave background, as well as large scale structures, can be evaded in this
model. This scenario can be further constrained using multiple terrestrial
experiments. In particular, for beta-decay experiments like KATRIN, non-trivial
distortions to the electron spectrum can be induced, even when time-variation
is fast and gets averaged out. Furthermore, the presence of time-varying masses
of sterile neutrinos will alter the interpretation of light sterile neutrino
parameter space in the context of the reactor and gallium anomalies. In
addition, we also study the impact of such time-varying neutrino masses on
results from the BEST collaboration, which have recently strengthened the
gallium anomaly. If confirmed, we find that the time-varying neutrino mass
hypothesis could give a better fit to the recent BEST data.
