We study models in which neutrino masses are generated dynamically at cosmologically late times. Our study is purely phenomenological and parameterized in terms of three effective parameters characterizing the redshift of mass generation, the width of the transition region, and the present day neutrino mass. We also study the possibility that neutrinos become strongly self-interacting at the time where the mass is generated. We find that in a number of cases, models with large present day neutrino masses are allowed by current CMB, BAO and supernova data. The increase in the allowed mass range makes it possible that a non-zero neutrino mass could be measured in direct detection experiments such as KATRIN. Intriguingly we also find that there are allowed models in which neutrinos become strongly self-interacting around the epoch of recombination.
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