Gravitational waves from walls bounded by strings in $SO(10)$ model of pseudo-Goldstone dark matter

We explore the gravitational wave spectrum generated by string-wall structures in an $SO(10)$ ($Spin(10)$) based scenario of pseudo-Goldstone boson dark matter (pGDM) particle. This dark matter candidate is a linear combination of the Standard Model (SM) singlets present in the 126 and 16 dimensional Higgs fields. The Higgs $126$-plet vacuum expectation value (VEV) $\left$ leaves unbroken the $\mathbb{Z}_2$ subgroup of $\mathbb{Z}_4$, the center of $SO(10)$. Among other things, this yields topologically stable cosmic strings with a string tension $\mu \sim \left^2$. The subsequent (spontaneous) breaking of $\mathbb{Z}_2$ at a significantly lower scale by the $16$-plet VEV $\left$ leads to the appearance of domain walls bounded by the strings produced earlier. We display the gravitational wave spectrum for $G \mu$ values varying between $10^{-15}$ and $10^{-9}$ ($\left\sim 10^{11}$ - $10^{14}$ GeV), and $\left\sim 0.1$ - $10^2$ TeV range ($G$ denotes Newton's constant.) These predictions can be tested, as we show, by a variety of (proposed) experiments including LISA, ET, CE and others.Comment: 8 pages, 3 figures, version published in PL