PeV-Scale SUSY and Cosmic Strings from F-term Hybrid Inflation

We consider F-term hybrid inflation (FHI) and SUSY breaking in the context of a B-L extension of MSSM which largely respects a global U(1) R symmetry. The hidden sector Kaehler manifold enjoys an enhanced SU(1,1)/U(1) symmetry with the scalar curvature determined by the achievement of a SUSY-breaking de Sitter vacuum without ugly tuning. FHI turns out to be consistent with data, provided that the magnitude of the emergent soft tadpole term is confined in the range (1.2-100) TeV, and it is accompanied with the production of B-L cosmic strings. If these are metastable they interpret the present observations from PTA experiments on the stochastic background of gravitational waves with dimensionless tension Gmu~(1-9.2)x10^-8. The mu parameter of MSSM arises by appropriately adapting the Giudice-Masiero mechanism and facilitates the out-of-equilibrium decay of the R saxion at a reheat temperature lower than about 71 GeV. Due to the prolonged matter dominated era the gravitational wave signal is suppressed at high frequencies. The SUSY mass scale turns out to lie in the PeV region.