Detectability of Gravitational Waves from Phase Transitions

TL;DR

This work addresses the detectability of a stochastic gravitational-wave background from first-order phase transitions in the early universe, focusing on the electroweak scale. It develops a semi-analytic framework that combines three GW sources—bubble collisions, hydrodynamic turbulence, and an MHD inverse cascade—parameterized by $T_*$, $g_*$, $\alpha$, $\beta$, and $\zeta_*$ to predict the total spectrum in terms of $h_c(f)$. By comparing to the LISA sensitivity curve, the authors map regions of phase-transition parameter space where a detectable signal is possible, highlighting that turbulence and magnetic helicity can substantially widen the accessible space beyond bubble collisions alone. The results suggest that electroweak-scale first-order transitions in many beyond-Standard-Model scenarios could leave a measurable imprint in the stochastic GW background, offering a direct probe of high-energy physics through gravitational waves.

Abstract

Gravitational waves potentially represent our only direct probe of the universe when it was less than one second old. In particular, first-order phase transitions in the early universe can generate a stochastic background of gravitational waves which may be detectable today. We briefly summarize the physical sources of gravitational radiation from phase transitions and present semi-analytic expressions for the resulting gravitational wave spectra from three distinct realistic sources: bubble collisions, turbulent plasma motions, and inverse-cascade helical magnetohydrodynamic turbulence. Using phenomenological parameters to describe phase transition properties, we determine the region of parameter space for which gravitational waves can be detected by the proposed Laser Interferometer Space Antenna. The electroweak phase transition is detectable for a wide range of parameters.

Figures (11)

• Figure 1: The spectrum of gravitational radiation for a first-order phase transition with $g_*=100$, $T_*=100\,{\rm GeV}$, $\alpha=0.5$ and $\beta=100H_\star$, from bubble collisions (dash line), hydrodynamic turbulence with zero helicity (solid line) and MHD turbulence with $\zeta_*=0.15$ (dash-dotted line). The bold solid line corresponds to the 1-year, 5$\sigma$ LISA sensitivity curve curve, including the confusion noise from white dwarf binaries whitedwarfs.
• Figure 2: The total spectrum of gravitational radiation (including there sources of gravitational radiation bubble collisions, hydro-turbulence, and MHD turbulence) for $g_\ast=100$, $T_\ast=100$ GeV, $\zeta_\ast=0.1$, $\beta=100 H_\ast$, and three different values of $\alpha$: $\alpha=1$ (solid line), $\alpha=0.5$ (dash line) and $\alpha=0.2$ (dotted line), with the LISA sensitivity curve..
• Figure 3: The total spectrum of gravitational radiation for $g_\ast=100$, $\alpha=0.5$, $\beta=100 H_\ast$, $\zeta_\ast =0.1$, and three different temperature values, $T_\ast=100\, {\rm GeV}$ (solid line), $T_\ast=1\, {\rm TeV}$ (dash line), and $T_\ast=10\, {\rm TeV}$ (dotted line), with the LISA sensitivity curve.
• Figure 4: The total spectrum of gravitational radiation for $g_\ast=100$, $T_\ast=100\,{\rm GeV}$, $\alpha_\ast=0.5$, $\beta=100H_\ast$, and four different values of $\zeta_\ast$: $\zeta_\ast=0$, corresponding to hydrodynamic turbulence without the inverse cascade effect (solid line), $\zeta_*=0.02$ (dash line), $\zeta_*=0.5$ (dotted line), and $\zeta_*=0.15$ (dot-dash line), with the LISA sensitivity curve.
• Figure 5: The total spectrum of gravitational radiation for $g_\ast=100$, $T_\ast=100\,{\rm GeV}$, $\zeta_\ast=0.1$, $\alpha=0.5$, and three different values of $\beta$: $\beta=40 H_\ast$ (solid line), $\beta=100 H_\ast$ (dash line) and $\beta=500 H_\ast$ (dotted line), with the LISA sensitivity curve.