F-Term Hybrid Inflation, Metastable Cosmic Strings and Low Reheating in View of ACT

Abstract

We consider the formation of metastable cosmic strings in a left-right unified theory. The produced monopoles are diluted by a stage of F-term hybrid inflation (FHI) which is realized consistently with the SUSY breaking and a global $U(1)$ $R$ symmetry in the context of a $U(1)_{\rm R}\times U(1)_{B-L}$ extension of MSSM. 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 compatible with data -- including the recent ACT results --, provided that the magnitude of the emergent soft tadpole term is confined in the range $(0.1-70)$ TeV, and it is accompanied with the production of cosmic strings. Their dimensionless tension $G\mu_{\rm cs}\simeq(1-11)\cdot10^{-8}$ interprets the present observations from PTA experiments on the stochastic background of gravitational waves. 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 $34$ GeV. The SUSY mass scale turns out to lie in the PeV region.