Gravitational Waves from Phase Transition in a Supersymmetric Left-Right Model

We investigate the cosmological phase transition dynamics in a supersymmetric left-right symmetric model based on the gauge group $SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ that addresses the strong CP problem through extended parity symmetry and doublet-doublet splitting. We compute the finite temperature effective potential including one-loop Coleman-Weinberg corrections, thermal contributions, and daisy resummation to determine whether the $SU(2)_R \times U(1)_{B-L} \to U(1)_Y$ symmetry breaking transition can produce observable gravitational waves. For phenomenologically viable parameters satisfying current LHC constraints, we find that the phase transition is strongly first-order with nucleation temperature $T_n \sim 0.5 v_R$, transition strength parameter $\alpha \sim 0.01-0.3$, and inverse duration $\beta/H \sim 100$. The resulting stochastic gravitational wave background peaks at frequencies $f \sim 0.1-1$ Hz with amplitude $h^2\Omega_{GW} \sim 10^{-14}-10^{-12}$. We find that there is a parameter region where the gravitational wave spectrum overlaps with DECIGO/BBO sensitivity curves, providing a potentially observable signature connecting the theoretical solution to the strong CP problem with gravitational wave experiments.