Gravitational Waves from the Phase Transition of a Non-linearly Realised Electroweak Gauge Symmetry

TL;DR

This work analyzes a non-linearly realised electroweak framework where the Higgs is a gauge-singlet with an anomalous cubic coupling $\kappa$, which can trigger a strongly first-order electroweak phase transition. Using a full one-loop finite-temperature potential and bubble-nucleation formalism, the authors compute phase-transition parameters and GW spectra from bubble collisions, sound waves, and MHD turbulence, finding a viable $|\kappa|$ window around $[111,118]$ GeV that yields detectable GWs in the millihertz range for eLISA (and broader sensitivity for BBO). The results indicate that such a cosmological signal could complement collider probes of the Higgs cubic coupling, and that future space-based GW detectors could reveal the nature of electroweak symmetry breaking in this scenario. The analysis highlights the interplay between model parameters, phase-transition dynamics, and GW detectability, emphasizing run-away bubble walls and the dominance of collisions in the predicted spectra within the explored parameter space.

Abstract

Within the Standard Model with non-linearly realised electroweak symmetry, the LHC Higgs boson may reside in a singlet representation of the gauge group. Several new interactions are then allowed, including anomalous Higgs self-couplings, which may drive the electroweak phase transition to be strongly first-order. In this paper we investigate the cosmological electroweak phase transition in a simplified model with an anomalous Higgs cubic self- coupling. We look at the feasibility of detecting gravitational waves produced during such a transition in the early universe by future space-based experiments. We find that for the range of relatively large cubic couplings, $111~{\rm GeV}~ \lesssim |κ| \lesssim 118~{\rm GeV}$, $\sim $mHz frequency gravitational waves can be observed by eLISA, while BBO will potentially be able to detect waves in a wider frequency range, $0.1-10~$mHz.

Figures (3)

• Figure 1: The finite temperature effective potential for cubic couplings taking the values (\ref{['fig:p125']}) $\kappa = -1.25 m_h^2/|v|$, (\ref{['fig:p15']}) $\kappa=-1.50 m_h^2/|v|$, (\ref{['fig:p175']}) $\kappa=-1.75 m_h^2/|v|$, (\ref{['fig:p185']}) $\kappa =-1.85 m_h^2/|v|$. The potential are shown for temperatures above and below that of $T_c$, as well as $T_c$ itself.
• Figure 2: The numerical results for the Euclidean action vs temperature for applicable values of cubic couplings, $\kappa$.
• Figure 3: Gravitational wave spectral energy density for a range of $\kappa$ values showing the individual contributions from each production mechanism and an approximate total. The sensitivity curves for relevant space-based detectors are given by the shaded regions. The purple shaded regions denote the eLISA configurations C1 to C4 (see (\ref{['app:eLISA']})), the light green shaded region corresponds DECIGO and the grey curve to BBO. The cubic coupling $\kappa$ for each graph are as follows (\ref{['fig:k125']}) $-1.25 m_h^2/|v|$, (\ref{['fig:k15']}) $-1.50 m_h^2/|v|$, (\ref{['fig:k175']}) $-1.75 m_h^2/|v|$ and (\ref{['fig:k185']}) $-1.85 m_h^2/|v|$.