A minimal Pati-Salam theory: from cosmic defects to gravitational waves and colliders

We discuss a minimal renormalizable Pati-Salam theory based on the $SU(4)_{\rm C}\,\times\,SU(2)_{\rm L}\,\times\,SU(2)_{\rm R}$ gauge group, with unification scale Higgs multiplets taken as $SU(2)_{\rm L}$ and $SU(2)_{\rm R}$ doublets, which lead to neutrino Dirac picture. Although a number of scalar particles could be light, even lying at the LHC energies, the unification scale is hopelessly out of reach in any foreseeable future. Moreover, phase transition in the early Universe leads to the production of magnetic monopoles and domain walls, both incompatible with the standard cosmological model. A small explicit breaking of the discrete left-right symmetry allows the domain walls to decay, and in the process possibly sweep away the monopoles, analogously to the previously discussed case of $SU(5)$ grand unified theory. This leaves an important imprint of gravitational waves, within the reach of next generation searches, correlated with monopole detection and new light particles at collider energies. The theory has a dark matter candidate in the form of an inert scalar doublet, with a mass below TeV, which can further trigger electroweak baryogenesis.