I'm puzzled why, now that we know that neutrinos have mass, we still read that there are only left-handed neutrinos, as far as we know. I understand that right-handed neutrinos do not interact by the weak force, so we would not detect them. My question is why we read that they might not / probably do not even exist. With electrons, their mass couples their left- and right-handed chiral states, so they oscillate between the two. If they are Dirac particles, shouldn't neutrinos do the same? Is it observationally permitted that the Universe is filled with right-handed neutrinos (either primordial or having oscillated from the left-handed chirality), or do are there constraints from, for instance, cosmic neutrino detectors or cosmology that rule this out?