Gravitational waves from metastable cosmic strings in the delayed scaling scenario

Recent observations by pulsar timing arrays (PTAs) such as NANOGrav, EPTA, PPTA, and CPTA suggest the presence of nanohertz stochastic gravitational wave background (GWB). While such signals could be explained by gravitational waves from a network of metastable cosmic strings (CSs), standard scenarios involving the Kibble-Zurek mechanism triggered by a thermal potential face significant challenges. Specifically, these scenarios predict a GWB spectrum inconsistent with the non-detection at higher frequencies by LIGO-Virgo-KAGRA (LVK) for CSs with relatively large string tension. It is also difficult to prevent the monopole forming phase transition just before the CS forming symmetry breaking, which spoils the CS network formation. In contrast, a delayed scaling scenario, where the CSs start to emit GWs at a later time due to the dilution during inflation, alleviates these issues. This scenario allows for a larger string tension while monopoles are sufficiently diluted such that the CS network safely forms. In this study, we clarify the spectrum of stochastic GWB from metastable CSs in the delayed scaling scenario, consistent with the PTA observations while satisfying the LVK constraints. Furthermore, we explore its potential signatures at frequencies accessible to other detectors such as LVK as well as LISA, Taiji, and TianQin or DECIGO and BBO. We also discuss the implications on inflation and underlying UV theories, such as the grand unified theories.