Gravitational waves from the electroweak phase transition

TL;DR

This work analyzes gravitational waves from the electroweak phase transition, incorporating full bubble dynamics, wall friction, and the possibility of different wall propagation modes across Standard Model extensions. It assesses GW production from both bubble collisions and turbulence, finding turbulence tends to dominate and runaway walls require significant parameter tuning. By applying bag-type thermodynamics and detailed friction calculations to scenarios with extra scalars, the MSSM, and strongly coupled fermions, the authors map the peak frequency and amplitude of the GW spectrum and compare them to planned detectors like LISA, NGO/eLISA, BBO, and DECIGO. The key result is that most SM-extensions yield GW signals below LISA's sensitivity, but strongly coupled scalar extensions can produce signals near LISA’s low-frequency edge with amplitudes up to $h^2\Omega_{GW}\sim 10^{-8}$ at $f\sim 10^{-4}$ Hz, while MSSM scenarios are unlikely to be detected without next-generation observatories. Overall, the paper highlights the crucial role of hydrodynamics, bubble size, and friction in shaping the electroweak GW signal and identifies a narrow parameter window where detection by future space-based detectors may be feasible.

Abstract

We study the generation of gravitational waves in the electroweak phase transition. We consider a few extensions of the Standard Model, namely, the addition of scalar singlets, the minimal supersymmetric extension, and the addition of TeV fermions. For each model we consider the complete dynamics of the phase transition. In particular, we estimate the friction force acting on bubble walls, and we take into account the fact that they can propagate either as detonations or as deflagrations preceded by shock fronts, or they can run away. We compute the peak frequency and peak intensity of the gravitational radiation generated by bubble collisions and turbulence. We discuss the detectability by proposed spaceborne detectors. For the models we considered, runaway walls require significant fine tuning of the parameters, and the gravitational wave signal from bubble collisions is generally much weaker than that from turbulence. Although the predicted signal is in most cases rather low for the sensitivity of LISA, models with strongly coupled extra scalars reach this sensitivity for frequencies $f\sim 10^{-4}\,\mathrm{Hz}$, and give intensities as high as $h^2Ω_{\mathrm{GW}}\sim 10^{-8}$.

Figures (11)

• Figure 1: The wall velocity (solid line) and shock velocity (dashed line) as functions of the friction, for $\alpha_c=4.45\times 10^{-3}$ and $\alpha_o=7.06\times 10^{-3}$.
• Figure 2: The inverse time scales and the bounce action, for an extension of the SM with a complex scalar singlet with coupling $h_s$ to the Higgs and invariant mass $\mu_s =0$. Red lines are calculated at $t=t_i$, black lines at $t=t_p$, and the blue line corresponds to $t_p-t_i$.
• Figure 3: The radius of the largest bubbles at $t=t_p$ and the different approximations, for the same model and parameters of Fig. \ref{['figbeta']}. Black lines correspond to the bubble wall and red lines to the shock wall. The parameter $\beta$ is calculated at the initial temperature $T_i$.
• Figure 4: Several quantities calculated at the beginning of bubble nucleation, as functions of $h_s$ for $g_s=2$ and $\mu_s =0$: the temperature and field mean value (upper left), the supercooling time $t_i-t_c$ (upper right), the bubble wall and shock velocities (lower left), and the kinetic energy of the fluid (lower right).
• Figure 5: The energy density (top) and frequency (bottom) at the peak of the GW spectrum from turbulence, as a function of $h_s$ for $g_s=2$ (rightmost curves) and $g_s=12$ (leftmost curves), with $\mu_s =0$ (solid lines), $100\, \mathrm{GeV}$ (dashed lines), and $200 \, \mathrm{GeV}$ (dotted lines). Horizontal dotted lines indicate the approximate values corresponding to the peak sensitivity of LISA and eLISA, $f\sim 1 \,\mathrm{mHz}$, $h^{2}\Omega_{\mathrm{GW}}\approx 5\times 10^{-12}$ for LISA, $h^{2}\Omega_{\mathrm{GW}}\approx 2\times 10^{-10}$ for eLISA.