Gravitational wave emission from metastable current-carrying strings in $E_6$

We discuss $E_6$ based extensions of the Standard Model (SM) containing two varieties of superheavy metastable cosmic strings (CSs) that respectively have neutral and electrically charged current carriers. We employ an extended version of the velocity-dependent one-scale (VOS) model, recently discussed by some authors, to estimate the gravitational wave (GW) spectrum emitted by metastable strings with a dimensionless string tension $G μ\approx 10^{-6}$ that carry a right-handed neutrino (RHN) current. We find that with a low to moderate amount of current, the spectrum is compatible with the LIGO O3 run and also consistent at the 1$σ$ level with the recent PTA signals.