Probing beyond the Standard Model with gravitational waves from phase transitions

TL;DR

The paper reviews how stochastic gravitational waves from first-order phase transitions can probe beyond-Standard-Model physics in the early Universe, outlining GW production mechanisms (bubble collisions, sound waves, turbulence, and topological defects) and the key PT parameters ($\alpha$, $\beta/H_*$, $v_w$, $K$) that shape the SGWB spectrum. It highlights the degeneracies in translating an observed SGWB into specific BSM models and discusses LISA prospects, including a geometric-parameter reconstruction approach validated by the LISA Cosmology Working Group results. The authors illustrate the strategy with two illustrative BSM scenarios (a real singlet with $\mathbb{Z}_2$ and a $U(1)_{B-L}$ extension), showing how LISA measurements can complement collider experiments despite intrinsic ambiguities. They stress the need for unified modeling and non-perturbative simulations to robustly predict SGWB spectra and to map observations onto fundamental theory, enabling meaningful discovery potential while acknowledging current limitations.

Abstract

This review article is based on a seminar presented at the Higgs pairs workshop 2025. Stochastic gravitational wave backgrounds can serve as probe of the diverse phenomenology encountered in beyond-Standard-Model scenarios featuring phase transitions in the early Universe. Focussing on gravitational wave production from first-order phase transitions, we present the main results of a recent analysis by the LISA Cosmology Working Group concerning the detectability of such signals with LISA. Strong degeneracies, both among the parameters controlling the phase transition and between these and the parameters of the beyond-Standard-Model scenario underlying the phase transition, complicate the reconstruction of the model from a potential signal. Nonetheless, once a specific scenario is assumed, LISA observations can supply constraints possibly complementary to those obtainable from present and future particle colliders.

Figures (6)

• Figure 1: Taken from Caprini:2024ofd. This figure shows the maximum signal to noise ratio (colour shading) among four GW observatories (PTAs with the SKA, LISA, Einstein Telescope and Cosmic Explorer) of the SGWB generated by a strong first-order PT in the parameter space given by the PT temperature $T_*$ and the inverse PT duration, $\beta/H_*$. The dashed lines show the SNR=5 curves for each detector, evaluated based on the detector noise only, without accounting for the presence of astrophysical foregrounds. The dotted lines show instead the SNR contours of the astrophysical foregrounds relevant in each detector's frequency range. More detail on the population of astrophysical sources taken into account for each detector is given in the main text. Within the region delineated by the dotted contours, the SNR of the cosmological signal exceeds the one of the foregrounds, and the former should therefore be readily detectable. Within the region bounded by the dashed contours, detection may still be achievable, depending on the detailed spectral shape of the cosmological signal. In the case of Einstein Telescope and Cosmic Explorer, the foregrounds lie below the detectors' noise, while for LISA the Galactic foreground component is higher than the detector noise, hence the reduction in accessible parameter space due to the foreground is larger (c.f. Caprini:2024ofd for more detail). For PTA, there is no dotted curve as the foreground corresponds to the SGWB that has been detected, and one should refer to the gray contour instead. Indeed, the gray contours denote the 95% confidence exclusion region from LVK non-detection of a SGWB Badger:2022nwo, and the 95% confidence region if the PTA NANOGrav signal is interpreted as originating from a strong first-order PT NANOGrav:2023hvm. The temperature intervals inferred from the intersection of the SNR curves of the different observatories with the $\beta/H_*=1$ axis correspond to those discussed in \ref{['sec:general']}, representing the energy scales in the early Universe at which each observatory can probe GW sources.
• Figure 2: Taken from Caprini:2024hue: SGWB power spectra from sound waves (dashed, coloured lines), MHD turbulence (dotted, coloured lines), and total, given by the sum of the two (solid, coloured lines), as a function of frequency. The black line in each panel shows the SGWB for the benchmark values of the parameters $K = 0.08$, $H_*\ell_* = 0.25$ (the notation of Caprini:2024hue is such that $R_*=\ell_*$), $v_w = 1$ (the notation is such that $\xi_w=v_w$), $T_* = 500$ GeV, $\epsilon = 0.5$. In each panel one parameter is varied around the benchmark value, while the others are kept fixed. The value of the varying parameter can be inferred from the colour shading of the horizontal bar. The gray dashed line appearing in each panel shows the forecasted noise curve of the LISA instrument.
• Figure 3: Taken from Caprini:2024hue: Template-based reconstruction of the thermodynamic parameters of a SGWB from bubble collisions at a strong first-order PT, together with the noise and foregrounds parameters. The posteriors of the direct sampling in terms of the thermodynamic parameters are shown in blue. The background red contours are reconstructed from a sample in terms of the geometric parameters of the broken power law, translated to thermodynamic parameters. The green contours are obtained from a Fisher analysis in terms of the geometric parameters, also translated to the thermodynamic parameters. The inset shows the injected noise, foregrounds and signal (dashed lines according to the legend), and their the reconstruction (shaded areas around the dashed lines).
• Figure 4: Taken from Caprini:2024hue: Template-based reconstruction of the thermodynamic parameters of a SGWB from sound waves and MHD turbulence at a moderately strong first-order PT, together with the noise and foreground parameters (note that the notation of Caprini:2024hue is such that $R_*=\ell_*$ and $\xi_w=v_w$). The posteriors of the direct sampling in terms of the thermodynamic parameters are shown in blue. The background red contours are reconstructed from a sample in terms of the geometric parameters of the double broken power law, and translated to the thermodynamic parameters. The green contours are obtained from a Fisher analysis in terms of the geometric parameters, also translated to the thermodynamic parameters. The inset shows the injected noise, foregrounds and signal (according to the legend), and their the reconstruction (shaded areas around the lines).
• Figure 5: All panels taken from Caprini:2024hue: LISA constraints on the SM extended with a $\mathbb{Z}_2$ gauge singlet.