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 the MSSM that largely respects a global $U\left(1\right)$R symmetry. The hidden sector Kaehler manifold enjoys an enhanced $SU(1,1)/U\left(1\right)$ symmetry, with the scalar curvature determined by the achievement of a SUSY-breaking de Sitter vacuum without undesirable tuning. FHI turns out to be consistent with the data, provided that the magnitude of the emergent soft tadpole term is confined to the range $(1.2$–$100)$ TeV, and it is accompanied by the production of $B-L$ cosmic strings. If these are metastable, they are consistent with the present observations from PTA experiments on the stochastic background of gravitational waves with dimensionless tension $G{\mu }_{\mathrm{cs}}\simeq (1-9.2)·{10}^{-8}$. The $\mu$ parameter of the 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.