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The dip model assumes that the ultra-high energy cosmic rays (UHECRs) above10$^{18}$ eV consist exclusively of protons and is consistent with the spectrumand composition measure by HiRes. Here we present the range of cosmogenicneutrino fluxes in the dip-model which are compatible with a recentdetermination of the extragalactic very high energy (VHE) gamma-ray diffusebackground derived from 2.5 years of Fermi/LAT data. We show that the largestfluxes predicted in the dip model would be detectable by IceCube in about 10years of observation and are within the reach of a few years of observationwith the ARA project. In the incomplete UHECR model in which protons areassumed to dominate only above 10$^{19}$ eV, the cosmogenic neutrino fluxescould be a factor of 2 or 3 larger. Any fraction of heavier nuclei in the UHECRat these energies would reduce the maximum cosmogenic neutrino fluxes. We alsoconsider here special evolution models in which the UHECR sources are assumedto have the same evolution of either the star formation rate (SFR), or thegamma-ray burst (GRB) rate, or the active galactic nuclei (AGN) rate in theUniverse and found that the last two are disfavored (and in the dip modelrejected) by the new VHE gamma-ray background.

Gamma-Ray Constraints on Maximum Cosmogenic Neutrino Fluxes and UHECR Source Evolution Models