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We study the CP domain walls and the consequent gravitational waves inducedby the spontaneous breaking of the CP symmetry in the complex singlet extensionto the Standard Model. We impose the constraints from the unitarity, stabilityand the global minimal of the vacuum solutions on the model parameter space.The CP domain wall profiles and tensions are obtained by numerically solvingthe relevant field equations. The explicit CP violation terms are thenintroduced to the potential as biased terms to make the domain walls unstableand collapse, The BBN bound on the magnitude of the energy bias is taken intoaccount. To achieve sufficiently strong gravitational wave signals, the domainwall tension $\sigma$ is required to be at least $\sigma/{\rm TeV}^3 \sim\mathcal{O}(10^3)$. We find that the gravitational wave spectrum can be probedin the future SKA and/or DECIGO programs, when the typical mass scale is atleast $\sim \mathcal{O}(10)$ TeV and the explicit CP violation terms are assmall as $\mathcal{O}(10^{-29}) - \mathcal{O}(10^{-27}) $. The gravitationalwaves from collapsing domain walls thus provide a complementarity to the probeof extremely small CP violation at high-energy scale.

The gravitational waves from the collapsing domain walls in the complex singlet model