We consider the effects of R-parity violation due to the inclusion of a bilinear μ′LHu superpotential term in high-scale supersymmetric models with an EeV scale gravitino as dark matter. Although the typical phenomenological limits on this coupling (e.g., due to lepton number violation and the preservation of the baryon asymmetry) are relaxed when the supersymmetric mass spectrum is assumed to be heavy (in excess of the inflationary scale of 3×1013 GeV), the requirement that the gravitino be sufficiently long lived so as to account for the observed dark matter density, leads to a relatively strong bound on μ′ 20 GeV. The dominant decay channels for the longitudinal component of the gravitino are Zν, W±l, and hν. To avoid an excess neutrino signal in IceCube, our limit on μ′ is then strengthened to μ′ 50 keV. When the bound is saturated, we find that there is a potentially detectable flux of monochromatic neutrinos with EeV energies.
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We thank W. Buchmuller for discussions. This work was supported by the France-US Projet International de Coopération Scientifique No. 06482 and PICS MicroDark. Y. M. acknowledges partial support from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie: RISE InvisiblesPlus (Grant Agreement No. 690575), the ITN Elusives (Grant Agreement No. 674896), and the ERC advanced grants Higgs@LHC. E. D. acknowledges partial support from the ANR Black-dS-String. The work of T. G., K. K., and K. A. O. was supported in part by the DOE Grant No. DE–SC0011842 at the University of Minnesota.