Cosmological phase transitions: from perturbative particle physics to gravitational waves

TL;DR

This review surveys the pipeline from particle-physics models to gravitational waves produced by first-order cosmological phase transitions. It emphasizes perturbative methods to construct the finite-temperature effective potential, compute transition rates via bounce solutions, and track bubble nucleation, percolation, and reheating in an expanding Universe. The authors synthesize how thermal parameters and hydrodynamics feed GW predictions for bubble collisions, sound waves, and turbulence, including gauge issues, resummation techniques, and three-dimensional EFT approaches. They discuss diverse beyond-Standard-Model scenarios (scalar singlets, $B-L$ extensions, axions) and assess GW detectability with current and planned observatories, highlighting uncertainties and open questions. Overall, the work provides a practical, physics-driven blueprint for predicting GW spectra from CSPTs and motivates further methodological developments to exploit GW observations as probes of new physics.

Abstract

Gravitational waves (GWs) were recently detected for the first time. This revolutionary discovery opens a new way of learning about particle physics through GWs from first-order phase transitions (FOPTs) in the early Universe. FOPTs could occur when new fundamental symmetries are spontaneously broken down to the Standard Model and are a vital ingredient in solutions of the matter anti-matter asymmetry problem. The purpose of our work is to review the path from a particle physics model to GWs, which contains many specialized parts, so here we provide a timely review of all the required steps, including: (i) building a finite-temperature effective potential in a particle physics model and checking for FOPTs; (ii) computing transition rates; (iii) analyzing the dynamics of bubbles of true vacuum expanding in a thermal plasma; (iv) characterizing a transition using thermal parameters; and, finally, (v) making predictions for GW spectra using the latest simulations and theoretical results and considering the detectability of predicted spectra at future GW detectors. For each step we emphasize the subtleties, advantages and drawbacks of different methods, discuss open questions and review the state-of-art approaches available in the literature. This provides everything a particle physicist needs to begin exploring GW phenomenology.

Figures (20)

• Figure 1: As the Universe cools, the potential develops a new minima away from the origin (left). A first-order phase transition occurs through bubbles, which appear spontaneously and expand in the thermal plasma (center). The GWs from bubble collisions and the plasma may be measured using a laser interferometer, resulting in a stochastic GW background spectrum (right).
• Figure 2: A two-dimensional Higgs potential with a circle of degenerate minima. A particular vacuum is chosen, breaking the symmetry.
• Figure 3: Possible shapes of the tree-level potential. The red line shows the shape of the potential given in \ref{['eq:phi_four']} when the parameter $m^2 > 0$, where in this case the minimum is located at the origin. The blue line shows the shape of the same potential when $m^2 < 0$, this is the well-known Mexican hat shaped potential of the Higgs mechanism with degenerate minima at non-zero values of the field $\phi$. Finally the yellow line shows a potential where there are two non-degenerate minima at different field locations and a barrier separating them, which is a shape that can appear already at tree-level when there is a cubic term in the potential.
• Figure 4: 1PI diagrams of scalar fields contributing to the one-loop effective potential in the simplest $\phi^4$ model.
• Figure 5: An illustration showing how applying the Legendre Transform twice maps the original function to its convex envelope (or hull). In this example we show a non-convex function labeled $V_{\text{1P1}}$ as a blue line, while the convex envelope of this function is shown by the dashed orange line and labeled $V_\text{eff}$. This is effectively an update of Figs. 3 and 4 appearing in ref. Dannenberg:1987fwDannenberg:1987fw, though for this illustration we have chosen $V_\text{1PI} = \phi^4 - 5.98 \phi^3 +12.94 \phi^2 -11.94\phi +4.98$, based on some mild modifications to the examples used for Fig. 1 in ref. Fujimoto:1982tcFujimoto:1982tc.