We analyze further implications of the existence of a massless boson - the Majoron - mainly coupled to left-handed neutrinos. Final lepton spectrum in pion leptonic decay is affected by Majoron bremsstrahlung, yielding a bound on Majoron-neutrino coupling from experimental data. Supernova dynamics is another issue discussed here. We address possible effects of the frequent neutrino-neutrino collisions, neutrino interconversion and light boson bremsstrahlung in neutrino scattering. In particular, we focus on the question of lepton number non-conservation. We find that deleptonization of the core and high-entropy collapse can occur, via a subtle interplay of neutrino interconversion and light boson bremsstrahlung. Then, we propose an unorthodox solution to the missing mass problem in the universe. Finally, we address the problem of galaxy formation, which appears in a new perspective within our model.