An upper bound to the supernova relic neutrino background from all past Type II supernovae is obtained using observations of the Universal metal enrichment history. We show that an unambiguous detection of these relic neutrinos by the Super-Kamiokande detector is unlikely. We also analyze the event rate in the Sudbury Neutrino Observatory (where coincident neutrons from anti-nu_e + D --> n + n + e+ might enhance background rejection), and arrive at the same conclusion. If the relic neutrino flux should be observed to exceed our upper bound and if the observations of the metal enrichment history (for z<1) are not in considerable error, then either the Type II supernova rate does not track the metal enrichment history or some mechanism may be responsible for transforming anti-nu_{mu,tau} --> anti-nu_e.
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