Constraining the cosmic strings gravitational wave spectra in no-scale inflation with viable gravitino dark matter and nonthermal leptogenesis

We revisit the hybrid inflation model gauged by U(1)B-L extension of the minimal supersymmetric standard model in a no-scale background. Considering a single predictive framework, we study inflation, leptogenesis, gavitino cosmology, and the stochastic background of gravitational waves produced by metastable cosmic strings. The spontaneous breaking of U(1)B-L at the end of inflation produces a network of metastable cosmic strings, while the interaction between the U(1)B-L Higgs field and the neutrinos generate heavy Majorana masses for the right-handed neutrinos. The heavy Majorana masses explain the tiny neutrino masses via the seesaw mechanism, a realistic scenario for reheating and nonthermal leptogenesis. We show that a successful nonthermal leptogenesis and a stable gravitino as a dark matter candidate can be achieved for a wide range of reheating temperatures and U(1)B-L symmetry breaking scales. The possibility of realizing metastable cosmic strings in a grand unified theory setup is briefly discussed. We find that a successful reheating with nonthermal leptogenesis and gravitino dark matter restricts the allowed values of string tension to a narrow range 10-9GμCS8×10-6, predicting a stochastic gravitational-wave background that lies within the 1σ bounds of the recent NANOGrav 12.5-yr data, as well as within the sensitivity bounds of future GW experiments.