We study the stochastic gravitational wave (GW) background resulting from the strong first-order phase transition (SFOPT) associated with $SU(2{)}_R\times U(1{)}_{B-L}$-breaking in the doublet left-right symmetric model (DLRSM). For different values of the symmetry-breaking scale $v_R=20$, 30, and 50 TeV, we construct the one-loop finite temperature effective potential to explore the parameter space for regions showing SFOPT. We identify the region where the associated GW background is strong enough to be detected at planned GW observatories. A strong GW signature favors a relatively light $CP$-even neutral scalar $H_3$, arising from the $SU(2{)}_R$ doublet. The $SU(2{)}_L$ subgroup of DLRSM is broken by three vacuum expectation values: ${\kappa }_1$, ${\kappa }_2$, and $v_L$. We observe a preference for $\mathcal{O}(1)$ values of the ratio $w=v_L/{\kappa }_1$, but no clear preference for the ratio $r={\kappa }_2/{\kappa }_1$. A large number of points with strong GW signal can be ruled out from precise measurement of the trilinear Higgs coupling and searches for $H_3$ at the future colliders.

• Received 20 November 2023
• Accepted 15 March 2024

DOI:https://doi.org/10.1103/PhysRevD.109.075034

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Published by the American Physical Society