Abstract
We consider a simple extension of Standard Model by adding two complex singlet scalars with a U(1) symmetry. A discrete $$ {\mathcal{Z}}_2\times {\mathcal{Z}}_2^{\prime } $$
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symmetry is imposed in the model and the added scalars acquire a non zero vacuum expectation value (VEV) when the imposed symmetry is broken spontaneously. The real (CP even) parts of the complex scalars mix with the SM Higgs and give three physical mass eigenstates. One of these physical mass eigenstates is attributed to the SM like Higgs boson with mass 125.09 GeV. In the present scenario, domain walls are formed in the early Universe due to the breaking of discrete $$ {\mathcal{Z}}_2\times {\mathcal{Z}}_2^{\prime } $$
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symmetry. In order to ensure the unstability of the domain wall this discrete symmetry is also explicitly broken by adding a bias potential to the Lagrangian. The unstable annihilating domain walls produce a significant amount of gravitational waves (GWs). In addition, we also explore the possibility of the production of GW emission from the strong first-order phase transition. We calculate the intensities and frequencies of each of such gravitational waves originating from two different phenomena of the early Universe namely annihilating domain walls and strong first-order phase transition. Finally, we investigate the observational signatures from these GWs at the future GW detectors such as ALIA, BBO, DECIGO, LISA, TianQin, Taiji, aLIGO, aLIGO+ and pulsar timing arrays such as SKA, IPTA, EPTA, PPTA, NANOGrav11 and NANOGrav12.5.