We consider inflation and supersymmetry breaking in the context of a minimal model of supersymmetry in which the only "low" energy remnant of supersymmetry is the gravitino with a mass of order an EeV. In this theory, the supersymmetry breaking scale is above the inflaton mass, m≃3×1013 GeV, as are all sfermion and gaugino masses. In particular, for a no-scale formulation of Starobinsky-like inflation using the volume modulus T, we show that inflation can be accommodated even when the supersymmetry breaking scale is very large. Reheating is driven through a gravitational coupling to the two Higgs doublets and is enhanced by the large μ-parameter. This leads to gravitino cold dark matter where the mass is constrained to be in the range 0.1 EeVm3/21000 EeV.
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We would like to thank Sebastian Ellis and Marco Peloso for helpful discussions. This work was supported by the France-US PICS No. 06482. Y. M. acknowledges partial support from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie: RISE InvisiblesPlus (Grant No. 690575), the ITN Elusives (Grant 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. and K. A. O. was supported in part by the DOE Grant No. DE–SC0011842 at the University of Minnesota.
© 2017 American Physical Society.