Gravitational waves from conformal symmetry breaking

TL;DR

The paper investigates gravitational waves from a strongly first-order electroweak phase transition in the classically conformal SU(2)cSM. It combines a full two-field finite-temperature effective potential with a gap-equation–based resummation to improve perturbativity, analyzes bubble nucleation, and computes the resulting GW spectrum. The results indicate large supercooling and GW signals well within LISA’s sensitivity, highlighting the model as a promising testbed for GW cosmology and particle phenomenology. It also identifies key uncertainties in phase-transition dynamics and motivates extending resummation techniques to the gauge sector and full 2PI treatment for more robust predictions.

Abstract

We consider the electroweak phase transition in the conformal extension of the standard model known as SU(2)cSM. Apart from the standard model particles, this model contains an additional scalar and gauge field that are both charged under the hidden SU(2)$_X$. This model generically exhibits a very strong phase transition that proceeds after a large amount of supercooling. We estimate the gravitational wave spectrum produced in this model and show that its amplitude and frequency fall within the observational window of LISA. We also discuss potential pitfalls and relevant points of improvement required to attain reliable estimates of the gravitational wave production in this - as well as in more general - class of models. In order to improve perturbativity during the early stages of transition that ends with bubble nucleation, we solve a thermal gap equation in the scalar sector inspired by the 2PI effective action formalism.

Figures (9)

• Figure 1: The trajectory of the global minimum of the effective potential in the $(h,\varphi)$ plane. The colours of the points indicate the temperature to which a given point corresponds. The plot in the right panel shows with better resolution the trajectory of the minimum after nonzero VEV for $\varphi$ is acquired. The colour coding is common for both of the plots.
• Figure 2: The bubble profile at the nucleation temperature.
• Figure 3: The contour plot of the effective potential at the nucleation temperature. In the left panel the true minimum is marked with the white dot, in the right panel the region around the symmetric minimum is shown, capturing the saddle point. Note that the colour coding is different in the two panels.
• Figure 4: Gravitational wave signals for the benchmark points analysed (solid lines), LISA sensitivity curves corresponding to different configurations (dashed lines).
• Figure 5: Comparison of the GW signals predicted with the use of the full two-field potential (solid line), the Gildener-Weinberg method (long-dashed line) and the potential along the $h=0$ direction (short-dashed line, overlaps the solid line).