  In models in which neutrinos are light, due to a low scale of symmetry
breaking, additional light bosons are generically present. We show that the
interaction between diffuse relic supernova neutrinos (RSN) and the cosmic
background neutrinos, via exchange of these light scalars, can result in a
dramatic change of the supernova (SN) neutrinos flux. Measurement of this
effect with current or future experiments can provide a spectacular direct
evidence for the low scale models. We demonstrate how the observation of
neutrinos from SN1987A constrains the symmetry breaking scale of the above
models. We also discuss how current and future experiments may confirm or
further constrain the above models, either by detecting the ``accumulative
resonance'' that diffuse RSN go through or via a large suppression of the flux
of neutrinos from nearby < O(Mpc) SN bursts.
