Inflation, proton decay and gravitational waves from metastable strings in SU(4) _<i>C</i> × SU(2) _<i>C</i> × SU(1) _<i>R</i> model

Abstract We present a realistic supersymmetric μ-hybrid inflation model within the framework of SU(4) C × SU(2) L × U(1) R gauge symmetry, wherein the symmetry breaking SU(4) C × SU(2) L × U(1) R → SU(3) C × SU(2) L × U(1) B-L × U(1) R occurs before observable inflation, effectively eliminating topologically stable primordial monopoles. Subsequent breaking of U(1) B-L × U(1) R → U(1) Y after inflation leads to the formation of superheavy metastable cosmic strings (CSs), capable of producing a stochastic gravitational wave background (SGWB) consistent with the recent PTA data. Moreover, the scalar spectral index n s and the tensor-to-scalar ratio r align with Planck 2018 observations. A consistent scenario for reheating and non-thermal leptogenesis is employed to explain the observed matter content of the universe. Finally, the embedding of G 421 into the Pati-Salam gauge symmetry G 422 is briefly discussed, predicting potentially observable proton decay rates detectable at facilities such as Hyper Kamiokande and DUNE.