C-parity, magnetic monopoles and higher frequency gravitational waves

We consider the spontaneous breaking of $SO(10)$ grand unified symmetry to the left-right symmetric model $SU(3{)}_c\times SU(3{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$ with C-parity also unbroken [$C$ converts $Q\to -Q$, where $Q$ is the electric charge operator in $SO(10)$.] This breaking produces the topologically stable GUT monopole as well as a GUT scale C-string. The subsequent breaking at an intermediate scale of C-parity produces domain walls bounded by C-strings, found by Kibble, Lazarides and Shafi. A limited number of inflationary $e$-foldings experienced during these breakings can yield an observable number density of primordial GUT monopoles. The C-strings also experience this inflationary phase, and the subsequent string-wall network decays through the emission of gravitational waves. We estimate the gravitational wave spectrum from these composite structures over a range of values of the domain wall tension $\sigma$. Depending on $\sigma$ the spectrum displays a peak in the higher frequency range between ${10}^2$ to ${10}^5$ Hz.