Gravitational Waves from Metastable Cosmic Strings in Supersymmetric New Inflation Model

Recent observations by pulsar timing arrays (PTAs) indicate a potential detection of a stochastic gravitational wave (GW) background. Metastable cosmic strings have been recognized as a possible source of the observed signals. In this paper, we propose an $R$-invariant supersymmetric new inflation model. It is characterized by a two-step symmetry breaking $\mathrm{SU}(2) \to \mathrm{U}(1)_G \to \mathrm{nothing}$, incorporating metastable cosmic strings. The field responsible for the initial symmetry breaking acts as the inflaton, while the second symmetry breaking occurs post-inflation, ensuring the formation of the cosmic string network without monopole production. Our model predicts symmetry breaking scales consistent with the string tensions favored by PTA data, $G_\mathrm{N} \mu_\mathrm{str} \sim 10^{-5}$, where $G_\mathrm{N}$ is the Newton constant. Notably, a low reheating temperature is required to suppress non-thermal gravitino production from the decay of inflaton sector fields. This also helps evading LIGO-Virgo-KAGRA constraints, while yielding a distinctive GW signature that future PTA and interferometer experiments can detect. Additionally, we examine the consistency of this scenario with non-thermal leptogenesis and supersymmetric dark matter.