Julien tells us about the cosmological effects of different neutrino mass states (i.e. the same sum of masses, but different masses for each individual neutrino – e.g. “normal” vs “inverted”).
There are effects, but they’re all very small and not even the best future experiments will distinguish them.
Non-standard model neutrinos would still have interesting effects, but it seems that cosmology’s insight on the SM ones will be limited to the sum of the masses.
Paper: https://arxiv.org/abs/2003.03354
Julien: https://lesgourg.github.io/