Gravitational Wave imprints of the Doublet Left-Right Symmetric Model

We study the gravitational wave (GW) signature in the doublet left-right symmetric model (DLRSM) resulting from the strong first-order phase transition (SFOPT) associated with $SU(2)_R\times U(1)_{B-L}$-breaking. 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 stochastic GW background is strong enough to be detected at planned GW observatories. A strong GW background favors a relatively light neutral CP-even scalar $H_{3}$, arising from the $SU(2)_R$ doublet. The $SU(2)_L$ subgroup of DLRSM is broken by three vevs: $\kappa_1,~\kappa_2$, 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 background can be ruled out from precise measurement of the trilinear Higgs coupling and searches for $H_3$ at future colliders.