Metastable Cosmic Strings and Gravitational Waves from Flavour Symmetry Breaking

Metastable cosmic strings (MSCSs) are among the best-fitting explanations of the 2023 pulsar timing array (PTA) signal for gravitational waves at nanohertz frequencies. We propose the novel possibility that a network of MSCSs generating this signal originates from the multi-step spontaneous breaking of a gauged flavour symmetry. As a specific example, we construct a model of $SU(2)$ flavour symmetry in the context of $SU(5)$ grand unification, where the $SU(2)$ acts exclusively on the first two generations of the matter 10-plet, such that it is ``right for leptons'' and allows for large lepton mixing. The model explains the mass hierarchies of the Standard Model fermions, and predicts the string scale of the MSCSs in a range compatible with the 2023 PTA signal. Cosmic inflation is associated with the latter step of (two-step) family symmetry breaking, and the phase transition ending inflation generates the cosmic string network.