Testing realistic SO(10) SUSY GUTs with proton decay and gravitational waves

We present a comprehensive analysis of a supersymmetric SO(10) grand unified theory, which is broken to the Standard Model via the breaking of two intermediate symmetries. The spontaneous breaking of the first intermediate symmetry, B - L, leads to the generation of cosmic strings and righthanded neutrino masses and further to an observable cosmological background of gravitational waves and generation of light neutrino masses via type -I seesaw mechanism. Supersymmetry breaking manifests as sparticle masses below the B - L breaking but far above the electroweak scale due to proton decay limits. This naturally pushes the B - L breaking scale close to the grand unified theory scale, leading to the formation of metastable cosmic strings, which can provide a gravitational wave spectrum consistent with the recent pulsar timing arrays observation. We perform a detailed analysis of this model using two -loop renormalization group equations, including threshold corrections, to determine the symmetry -breaking scale consistent with the recent pulsar timing arrays signals such as NANOGrav 15 -year data and testable by the next -generation limits on proton decay from Hyper -K and JUNO. Simultaneously, we find the regions of the model parameter space that can predict the measured quark and lepton masses and mixing, baryon asymmetry of our Universe, a viable dark matter candidate and can be tested by a combination of neutrinoless double beta decay searches and limits on the sum of neutrinos masses.