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

TL;DR

The paper investigates gravitational-wave production from a cosmological phase transition in a supersymmetric left-right model that addresses the strong CP problem via extended parity and doublet-doublet splitting. It computes the complete finite-temperature effective potential, including one-loop Coleman-Weinberg corrections, thermal effects, and daisy resummation, to show a strongly first-order $SU(2)_R\times U(1)_{B-L} \to U(1)_Y$ transition with $T_n \sim 0.5\,v_R$, $\alpha \sim 0.01-0.3$, and $\beta/H \sim 100$, yielding a GW spectrum peaked at $f \sim 0.1$--$1$ Hz and $h^2\Omega_{GW} \sim 10^{-14}$--$10^{-12}$. A region of parameter space exhibits overlap with DECIGO/BBO sensitivity curves, offering a potentially observable signature connecting a theoretical solution to the strong CP problem with gravitational-wave experiments. The work highlights how first-principles finite-temperature dynamics in a motivated BSM framework can lead to testable cosmological signals in upcoming space-based detectors, thereby linking high-scale parity-based CP violation mechanisms to observable gravitational waves.

Abstract

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 $α\sim 0.01-0.3$, and inverse duration $β/H \sim 100$. The resulting stochastic gravitational wave background peaks at frequencies $f \sim 0.1-1$ Hz with amplitude $h^2Ω_{GW} \sim 10^{-14}-10^{-12}$. 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.

Figures (3)

• Figure 1: Dependence of the nucleation temperature $T_n/v_R$ parameter on $\lambda$ for $g_R=g_L=0.655$. For other parameters, we fix $\xi = 5\times 10^8$ GeV, $k=0.01$, $m_H=10^3$ GeV, $Y_N=0.3$.
• Figure 2: Dependence of phase transition parameters $\alpha$ (Left) and $\beta/H$(Right) on $\lambda$$g_R=g_L=0.65$. For other parameters, we fix $\xi = 5\times 10^8$ GeV, $k=0.01$, $m_H=10^3$ GeV, $Y_N=0.3$.
• Figure 3: Gravitational wave spectrum: The black solid lines are the total spectrum. The green dotted lines are the sound waves, the red dashed-dotted lines are the bubble collisions, the blue dashed lines are the turbulence contributions. The LISA, DECIGO, BBO, ET sensitiviy lines are shown with the blue solid line, the yellow solid line, the green solid line, and the red solid lines. All panels assume $gR=gL=0.65$. (a).Left-upper Panel: $\lambda=0.05$, $\xi=5\times 10^8$ GeV. (b).Right-upper Panel: $\lambda=0.01$, $\xi= 10^8$ GeV. (c).Left-lower Panel: $\lambda=0.05$, $\xi=1.25\times 10^8$ GeV. (d).Right-lower Panel: $\lambda=0.01$, $\xi=2.5\times 10^8$ GeV.