  Models of late-time neutrino mass generation contain new interactions of the
cosmic background neutrinos with supernova relic neutrinos (SRNs) through
exchange of the on-shell light boson, leading to significant modification of
the differential SRN flux observed at earth. We consider Abelian U(1) model for
generating neutrino masses at low scales and we show that there is a large
parameter space in this model for which the changes induced in the flux by the
exchange of the light bosons might allow one to distinguish between neutrinos
being Majorana or Dirac particles, the type of neutrino mass hierarchy (normal
or inverted or quasi-degenerate), and could also possibly determine the
absolute values of the neutrino masses. Measurements of the presence of these
effects would be possible at the next-generation water Cerenkov detectors
enriched with Gadolinium, or a large 100 kton liquid argon detector.
