Model Discrimination in Gravitational Wave spectra from Dark Phase Transitions

TL;DR

This work analyzes gravitational-wave spectra from first-order phase transitions in dark sectors, focusing on two limiting potentials (renormalizable and non-renormalizable) and how spectral features depend on thermal parameters ($T_N$, $eta/H$, $\xi$). By mapping to concrete DM scenarios (generalized baryon number, atomic DM, composite DM), it demonstrates how GW observations could distinguish among hidden-sector models via the scale $v/\Lambda$, gauge content, and fermion couplings. The authors compute bounce solutions to derive thermal parameters, show that non-renormalizable operators substantially enhance GW visibility, and discuss how the GW peak properties relate to the underlying Lagrangian, with implications for DM relic abundance and cosmology. They also outline caveats (HT expansion validity, wall velocities) and future avenues, including full thermal function computations and multi-field extensions, highlighting the potential of LISA-era data to probe dark-phase-transition physics.

Abstract

In anticipation of upcoming gravitational wave experiments, we provide a comprehensive overview of the spectra predicted by phase transitions triggered by states from a large variety of dark sector models. Such spectra are functions of the quantum numbers and (self-) couplings of the scalar that triggers the dark phase transition. We classify dark sectors that give rise to a first order phase transition and perform a numerical scan over the thermal parameter space. We then characterize scenarios in which a measurement of a new source of gravitational waves could allow us to discriminate between models with differing particle content.

Figures (6)

• Figure 1: The potential \ref{['246potential']} at $T=0$ for the two limiting values of the parameter $\alpha$.
• Figure 2: (Schematically) the LISA inverse problem. In the above, the subscript $x$ refers to the dominant peak of the GW spectra (collision, sound wave, or turbulence). As described in the text, for most models the sound wave contribution is dominant. The thermal parameters of the PT can be calculated by solving the bounce EOM \ref{['eomsinglet']}, and then related to the GW spectra using \ref{['ampsw']} and \ref{['freqsw']}. This paper finds general relations between the GW spectra and the Lagrangian.
• Figure 3: Thermal parameters from the PT described by Eqs \ref{['234potential']} (left) and \ref{['246potential']} (right). The dominant contribution to the spectrum comes from the sound-wave term. The plot points are coloured by their effective zero temperature mass, found from $m^2 =d^2V/dT^2$ evaluated at $v$. The dashed contours in the plots correspond to the GW amplitude $\Omega_{\rm sw}$\ref{['ampsw']}, where we have chosen $v_w = 0.5$ in the left plot, and $v_w=1$ in the right plot (with the corresponding efficiencies from Espinosa:2010hh), as motivated using the conditions in Bodeker:2009qy. The upper thicker contour corresponds to the LISA 1-year peak sensitivity Moore:2014lga. The lower thicker dashed contour corresponds to LISA for a power-law spectrum (integrated over frequency), taken from Thrane:2013oya. The width of the contours is found from varying the zero-temperature potential parameters. Left: unless otherwise indicated, the number of Yukawa couplings is taken to be zero. If present, the Yukawa couplings are set to $y_\chi=1$. Right: unless otherwise indicated, $g=1$. The light blue dashed line corresponds to the predictions from the EWPT.
• Figure 4: Thermal parameters from the PT described by Eqs \ref{['234potential']} and \ref{['246potential']} respectively. The dashed contours in the plots correspond to the sound wave peak $f_{\rm sw}$\ref{['freqsw']}, where we have chosen the wall velocities as in Fig. \ref{['fig:amps']}. The thicker dashed contour corresponds to the LISA frequency peak Thrane:2013oya. Note that the EWPT results do not overlap with our scans, since the nucleation temperature $T_N$ is sensitive to the scale $\Lambda$.
• Figure 5: Thermal parameters from the PT described by Eqs \ref{['234potential']} (left) and \ref{['246potential']} (right). For the non-renormalizable potentials we take $\alpha =0.8$. In the cases where we vary $N_F$ we set $N=10(4)$, whereas in the cases where we vary $N$ we set $N_F=10(4)$ for the renormalizable and non-renormalizable potentials respectively. The black dashed line shows LISA visibility for a power spectrum integrated over frequency taken from Thrane:2013oya.