Gravitational Waves from Phase Transitions at the Electroweak Scale and Beyond

TL;DR

The paper investigates stochastic gravitational waves produced by first-order phase transitions across a wide range of temperatures, from the electroweak scale to well above, and develops a model-independent framework using the two parameters α (latent heat) and β/H* (transition duration) to predict the resulting GW spectra from bubble collisions and plasma turbulence. By scanning the (α, β/H*) plane at multiple temperatures, the authors map regions where LISA, BBO, and LIGO could detect these signals, incorporating astrophysical foregrounds and detector sensitivities. They find that electroweak-scale transitions may be detectable only in favorable model scenarios (e.g., NMSSM), while higher-temperature transitions could produce strong, detectable signatures, with some cases capable of masking the inflationary GW background. The work highlights the potential to use GW observations to constrain the scalar potentials governing electroweak symmetry breaking and beyond, offering a path to probe high-energy physics complementary to collider experiments.

Abstract

If there was a first order phase transition in the early universe, there should be an associated stochastic background of gravitational waves. In this paper, we point out that the characteristic frequency of the spectrum due to phase transitions which took place in the temperature range 100 GeV - 10^7 GeV is precisely in the window that will be probed by the second generation of space-based interferometers such as the Big Bang Observer (BBO). Taking into account the astrophysical foreground, we determine the type of phase transitions which could be detected either at LISA, LIGO or BBO, in terms of the amount of supercooling and the duration of the phase transition that are needed. Those two quantities can be calculated for any given effective scalar potential describing the phase transition. In particular, the new models of electroweak symmetry breaking which have been proposed in the last few years typically have a different Higgs potential from the Standard Model. They could lead to a gravitational wave signature in the milli-Hertz frequency, which is precisely the peak sensitivity of LISA. We also show that the signal coming from phase transitions taking place at T ~ 1-100 TeV could entirely screen the relic gravitational wave signal expected from standard inflationary models.

Figures (6)

• Figure 1: Spectrum of gravitational waves expected from a first order phase transition (solid blue line) for four temperatures and for some choices of ($\alpha, \beta/H$) values. The dashed red lines are the (approximate) predicted sensitivities of LISA, BBO, LIGO-III. The horizontal dashed green lines are the gravitational spectra expected from inflation, for two scales of inflation, for comparison. The black dashed curve is the estimate for the irreducible foreground due to white dwarf binaries (from Farmer:2003pa). At large $\alpha$, only the peak from turbulence can be seen as well as a change of slope (shown as a circled cross) corresponding to the high frequency tail of the bubble collision spectrum. For low $\alpha$, it is possible to see the collision peak as well.
• Figure 2: Different configurations of the signal versus the instrument sensitivity to show the qualitative dependence on parameters. The upper blue region is where the turbulence peak is observable while the lower red one is the region where either the collision peak or the point of slope change is visible. Precise locations of these different regions depend on the experiment and the temperature of the transition as illustrated in Figs. \ref{['fig:LISAcontours']}, \ref{['fig:BBO']} and \ref{['fig:LIGOcontours']}.
• Figure 3: Contours delimiting the region in the ($\alpha$, $\beta/H$) plane for which there is an observable peak at LISA. The upper blue region is for the turbulence peak while the lower red one is the region where either the collision peak or the point of slope change is visible. Left of the vertical green line, the collision peak is visible.
• Figure 4: Same as Fig. \ref{['fig:LISAcontours']} but for BBO. The effect of including the constraint from the irreducible WD foreground is displayed and limits the observable regions from the uncolored ones to the ones in plain colors. As the temperature increases, the peaks are shifted to higher frequencies, thus the effect of the WD foreground becomes less significant.
• Figure 5: Same as Fig. \ref{['fig:LISAcontours']} but for LIGO-III.