  Within the framework of the Standard Model of particle physics and standard
cosmology, observations of the Cosmic Microwave Background (CMB) and Baryon
Acoustic Oscillations (BAO) set stringent bounds on the sum of the masses of
neutrinos. If these bounds are satisfied, the upcoming KATRIN experiment which
is designed to probe neutrino mass down to $\sim 0.2$ eV will observe only a
null signal. We show that the bounds can be relaxed by introducing new
interactions for the massive active neutrinos, making neutrino masses in the
range observable by KATRIN compatible with cosmological bounds. Within this
scenario, neutrinos convert to new stable light particles by resonant
production of intermediate states around a temperature of $T\sim$ keV in the
early Universe, leading to a much less pronounced suppression of density
fluctuations compared to the standard model.
