Gravitational Waves from Electroweak Phase Transitions

TL;DR

The paper assesses stochastic gravitational-wave backgrounds from electroweak-scale phase transitions in supersymmetric models and their detectability by LISA. It analyzes two production channels—bubble collisions and turbulence—using a thermal effective potential to compute $\alpha$, $\beta$, and the bubble action $S_3(T)$ in the MSSM and NMSSM. Results show the MSSM yields signals far below LISA sensitivity, while the NMSSM can produce $h_0^2\Omega_{\rm gw}$ up to $\sim 10^{-10}$ from collisions and $\sim 10^{-9}$ from turbulence, with a peak near $f\sim 10$ mHz, potentially within LISA’s reach. The findings link the strength of the gravitational-wave signal to regions of parameter space that also support electroweak baryogenesis, highlighting the NMSSM as a testable framework via gravitational waves.

Abstract

Gravitational waves are generated during first-order phase transitions, either by turbolence or by bubble collisions. If the transition takes place at temperatures of the order of the electroweak scale, the frequency of these gravitational waves is today just within the band of the planned space interferometer LISA. We present a detailed analysis of the production of gravitational waves during an electroweak phase transition in different supersymmetric models where, contrary to the case of the Standard Model, the transition can be first order. We find that the stochastic background of gravitational waves generated by bubble nucleation can reach a maximum value h0^2 Omega_{gw} of order 10^{-10} - 10^{-11}, which is within the reach of the planned sensitivity of LISA, while turbolence can even produce signals at the level h0^2 Omega_{gw} \sim 10^{-9}. These values of h0^2 Omega_{gw} are obtained in the regions of the parameter space which can account for the generation of the baryon asymmetry at the electroweak scale.

Figures (20)

• Figure 1: Typical temperature-dependence of the potential $V$ for a scalar field $\phi$ driving a first order transition. The dotted curve refers to very high temperature, while longer dashed lines refer to lower temperatures. $T_1$ is the temperature at which a minimum at $\langle \phi \rangle \neq 0$ develops; at $T_{\rm deg}$ the two minima are degenerate; at $T_{\rm dest}$ the origin $\langle \phi \rangle = 0$ becomes unstable. The actual transition temperature $T_*$ is between $T_{\rm dest}$ and $T_{\rm deg}$.
• Figure 2: Typical profile of a bubble solution $\phi_b (r)$ interpolating from the true vacuum phase at $r=0$ to the false vacuum at $r=\infty$. The solution shown corresponds to the critical bubble at the transition temperature in the MSSM for $\sin^2 \beta_{{\rm MSSM}} = 0.8$, $m_{\rm Higgs}=110$ GeV and $m_{{\rm stop}}=140$ GeV, see section II.
• Figure 3: Overshooting-undershooting method.
• Figure 4: The plot shows the rapid variation experienced by the action $S_3(T)/T$ (evaluated on critical bubble solutions) in a small range of temperature: $S_3(T)/T$ moves from 0 to $\infty$ going from $T = T_{\rm dest}$ to $T = T_{\rm deg}$, with $(T_{\rm deg} - T_{\rm dest}) / T_{\rm dest} \sim 1 \%$. The particular case shown in the figure refers to the electroweak transtion in the MSSM with $m_{\rm Higgs}=110$ GeV, $m_{{\rm stop}}=145$ GeV, $\sin^2 \beta_{{\rm MSSM}}=0.8$, see section II.
• Figure 5: Contour plot of $\alpha$ as a function of the Higgs and stop masses for $\sin^2 \beta = 0.8$. The shaded region is forbidden by the request of absence of color breaking minima. $\alpha$ is computed at the destabilization temperature, as discussed in the text. ${}^{}$