Explaining PTA results by metastable cosmic strings from SO(10) GUT

In a recent paper (Phys. Rev. D 108 (2023) 095053), we have demonstrated that the 2023 PTA results, which hint at a stochastic gravitational wave (GW) background at nanohertz frequencies, point towards a promising model-building route for realizing SO(10) Grand Unification with embedded inflation. The proposed supersymmetric scenario solves the doublet-triplet splitting without fine-tuning, accounts for charged fermion and neutrino masses, avoids conflicts with current proton decay bounds, and includes only representations no larger than the adjoint. It features multi-step breaking of SO(10) to the Standard Model gauge symmetry, with inflation embedded such that metastable cosmic strings are produced at the end of inflation. This cosmic string network generates a stochastic GW background that can explain the PTA results. In this paper, we provide a detailed analysis of the singled out GUT model class, focusing on how the gauge coupling unification condition affects the scales of multi-step SO(10) breaking and the preferred GW spectra. The lowest breaking scale, linked to inflation, the generation of right-handed neutrino masses for the seesaw mechanism, and metastable cosmic string production, coincides with the range suggested by the PTA results.