We consider theories in which the generation of neutrino masses is associated with the breaking of an approximate global lepton number symmetry. In such a scenario the spectrum of light states includes the Majoron, the pseudo-Nambu Goldstone boson associated with the breaking of the global symmetry. For a broad range of parameters, the Majoron decays to neutrinos at late times, after the cosmic neutrinos have decoupled from the thermal bath, resulting in a secondary contribution to the cosmic neutrino background. We determine the current bounds on this scenario, and explore the possibility of directly detecting this secondary cosmic neutrino background in experiments based on neutrino capture on nuclei. For Majoron masses in the eV range or below, the neutrino flux from these decays can be comparable to that from the primary cosmic neutrino background, making it a promising target for direct detection experiments. The neutrinos from Majoron decay are redshifted by the cosmic expansion, and exhibit a characteristic energy spectrum that depends on both the Majoron mass and its lifetime. For Majoron lifetimes of order the age of the universe or larger, there is also a monochromatic contribution to the neutrino flux from Majoron decays in the Milky Way that can be comparable to the diffuse extragalactic flux. We find that for Majoron masses in the eV range, direct detection experiments based on neutrino capture on tritium, such as PTOLEMY, will be sensitive to this scenario with 100 gram-years of data. In the event of a signal, the galactic and extragalactic components can be distinguished on the basis of their distinct energy distributions, and also by using directional information obtained by polarizing the target nuclei.
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