  In this work, we construct promising model building routes towards SO(10) GUT
inflation and examine their ability to explain the recent PTA results hinting
at a stochastic gravitational wave (GW) background at nanohertz frequencies. We
consider a supersymmetric framework within which the so-called doublet-triplet
splitting problem is solved without introducing fine-tuning. Additionally,
realistic fermion masses and mixings, gauge coupling unification, and cosmic
inflation are incorporated by utilizing superfields with representations no
higher than the adjoint representation. Among the three possible scenarios, two
of these cases require a single adjoint Higgs field, and do not lead to cosmic
strings. In contrast, the third scenario featuring two adjoints, can lead to a
network of metastable cosmic strings that generates a GW background
contribution compatible with the recent PTA findings and testable by various
ongoing and upcoming GW observatories.
