Gravitational waves from a first order electroweak phase transition: a brief review

TL;DR

This review analyzes gravitational-wave production from a first-order electroweak phase transition, focusing on bubble dynamics and their coupling to the primordial plasma. It integrates envelope-approximation results for scalar-field collisions with field-fluid simulations to model three GW sources: colliding scalar shells, acoustic waves, and turbulence, expressing the spectra in terms of $\alpha_{T_*}$, $\beta/H_*$, $T_*$, and $v_w$. It highlights acoustic waves as the dominant source in thermal transitions and provides formulae to map specific beyond-Standard-Model scenarios to predicted power spectra, while noting important corrections and uncertainties in the sound-wave formula. The outlook emphasizes advancing nonperturbative thermodynamics, more extensive simulations, and the critical role of these predictions for future space-based detectors like LISA in probing new physics beyond colliders.

Abstract

We review the production of gravitational waves by an electroweak first order phase transition. The resulting signal is a good candidate for detection at next-generation gravitational wave detectors, such as LISA. Detection of such a source of gravitational waves could yield information about physics beyond the Standard Model that is complementary to that accessible to current and near-future collider experiments. We summarise efforts to simulate and model the phase transition and the resulting production of gravitational waves.

Figures (6)

• Figure 1: Cartoon showing features associated with the bubble wall. The scenario shown is a subsonic deflagration, where the wall speed $v_\mathrm{w}$ is slower than the speed of sound $c_\mathrm{s}$. The scalar field bubble wall is shown, while the 'sound shell' of nonzero fluid velocity in front of the wall is shaded. Above the diagram the value of $\langle \phi \rangle$ is shown, while below the radial fluid velocity $V_r$ is shown.
• Figure 2: Sketch of forces acting on bubble wall. The latent heat released during the phase transition drives the bubble outwards, while its interaction with the plasma of light particles creates friction. When the two forces are balanced, the wall ceases to accelerate.
• Figure 3: Efficiency $\kappa_\mathrm{f}$ measured (at points marked by circles) from spherically symmetric simulations of the field-fluid system for a single bubble by means of Eq. (\ref{['eq:efficiency']}) (Cutting 2017, private communication). There is agreement with the analytically computed efficiency curves and in Ref. Espinosa:2010hh, even though the authors of that work used a bag model rather than the Standard Model-like effective potential employed here.
• Figure 4: Sketch of a slice through a 'simulation' in the envelope approximation, with a spherical simulation volume. Only the uncollided portions of the thin bubble walls are recorded; there are no dynamics around the bubbles, or in the aftermath of bubble collisions.
• Figure 5: Portions of slices through a three-dimensional field-fluid simulation, with hotter colours indicating relatively higher fluid kinetic energies. Here $\alpha_{T_*} \approx 0.01$ and $v_\mathrm{w} \approx 0.68$. The slice at left shows mostly uncollided bubbles, while the slice at right is from long after the bubbles have collided.