Electroweak baryogenesis and gravitational waves from a real scalar singlet

TL;DR

This work analyzes a minimal SM extension with a real scalar singlet that enables a strong first-order electroweak phase transition and introduces CP violation through a dimension-6 operator modifying the top-quark mass. By solving transport equations for baryogenesis and computing the associated gravitational-wave spectrum from the phase transition, the authors reveal a robust correlation: larger new-physics scales Λ yield stronger gravitational waves while still achieving the observed baryon asymmetry. They demonstrate that future space-based detectors like LISA and BBO can probe the parameter space, including regions with high Λ, linking cosmological baryogenesis to observable gravitational waves. The study also highlights the role of two-step phase-transition dynamics and wall-velocity effects in shaping both η_B and the GW signal, offering conservative predictions and avenues for more detailed future work on bubble-wall dynamics.

Abstract

We consider a real scalar singlet field which provides a strong first-order electroweak phase transition via its coupling to the Higgs boson, and gives a $CP$ violating contribution on the top quark mass via a dimension-6 operator. We study the correlation between the baryon-to-entropy ratio produced by electroweak baryogenesis, and the gravitational wave signal from the electroweak phase transition. We show that future gravitational wave experiments can test, in particular, the region of the model parameter space where the observed baryon-to-entropy ratio can be obtained even if the new physics scale, which is explicit in the dimension-6 operator, is high.

Figures (7)

• Figure 1: Color coding shows the critical temperature in the region where the conditions for the first-order electroweak phase transition are fulfilled for $\lambda_{\rm s} = 0.1$. The dashed line shows the lower limit on $\lambda_{\rm hs}$ requiring that the extremum in the $s$ direction at $T=0.95T_c$ is a minimum. The gray region is excluded for $\lambda_{\rm s} = 0.1$ because there the $T=0$ global minimum of the potential is at $h=0$. In the white region the electroweak phase transition is not of first-order. The green contour marks off the region where the transition is of first-order for $\lambda_{\rm s} = 0.5$. The blue shaded region is excluded by the Higgs invisible decay.
• Figure 2: The bubble nucleation temperature $T_{\rm n}$ as a function of the critical temperature $T_{\rm c}$ for the points from the scan with $\lambda_{\rm s} = 0.1$. Color coding shows the strength of the transition, $v_{\rm n}/T_{\rm n}$. The dashed line corresponds to $T_{\rm n} = T_{\rm c}$. All points are allowed by the Higgs invisible decay.
• Figure 3: Points from the scan with $\lambda_{\rm s}=0.1$. Color coding shows the ratio of the bubble nucleation temperature $T_{\rm n}$ and the critical temperature $T_{\rm c}$. Here $L_{\rm w}$ denotes the bubble wall width, and $v_{\rm w}$ the relative velocity between the bubble wall and the plasma just in front of the wall. To the right of the vertical dashed lines, the transition is sufficiently strong to avoid baryon washout. The blue line in the right panel shows $v_{\rm w} = \xi_{\rm w} = 0.2$, and the blue points show the value of $v_{\rm w}$ for $\xi_{\rm w} = 0.34$.
• Figure 4: The same points as in the right panel of Fig. \ref{['hydr']}. The vertical axis shows the new physics scale $\Lambda$ which gives the observed baryon-to-entropy ratio. Color coding shows the ratio of released vacuum energy in the transition to that of the radiation bath at the bubble nucleation temperature.
• Figure 5: Blue lines show the values of the relative velocity between the bubble wall and the plasma just in front of the wall, $v_{\rm w}$, and the bubble wall width $L_{\rm w}$, which give baryon-to-entropy ratios shown in the plot. Here $\lambda_{\rm hs} = 0.554$, $\lambda_{\rm s} = 0.1$, $m_{\rm s} = 114.4$ GeV, and $\Lambda = 1.91$ TeV. Gray dotted lines show the values of $v_{\rm w}$ and $L_{\rm w}$ given by Eqs \ref{['vweq']} and \ref{['lweq']}.