Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions

TL;DR

This work quantitatively assesses eLISA's ability to detect a stochastic gravitational-wave background from strong first-order cosmological phase transitions. It combines envelope-approximation scalar-field signals with fluid-derived sound waves and MHD turbulence, and maps the GW predictions onto four representative eLISA configurations in a largely model-independent framework. The authors then test several well-motivated models—spanning electroweak-scale to beyond-electroweak-scale transitions—computing PT parameters and evaluating detectability, highlighting scenarios where eLISA can reveal physics inaccessible to colliders. The results show that six-link configurations offer the most comprehensive reach, with substantial sensitivity even to transitions at multi-TeV scales or in hidden/dilaton-like sectors, underscoring eLISA's potential as a complementary probe of early-Universe dynamics and new physics. Overall, the paper provides a practical methodology to translate PT dynamics into GW observables and outlines concrete benchmarks across diverse beyond-the-Standard-Model frameworks.

Abstract

We investigate the potential for the eLISA space-based interferometer to detect the stochastic gravitational wave background produced by strong first-order cosmological phase transitions. We discuss the resulting contributions from bubble collisions, magnetohydrodynamic turbulence, and sound waves to the stochastic background, and estimate the total corresponding signal predicted in gravitational waves. The projected sensitivity of eLISA to cosmological phase transitions is computed in a model-independent way for various detector designs and configurations. By applying these results to several specific models, we demonstrate that eLISA is able to probe many well-motivated scenarios beyond the Standard Model of particle physics predicting strong first-order cosmological phase transitions in the early Universe.

Figures (7)

• Figure 1: Sensitivity curves of the C1-C4 configurations given in Table \ref{['tab:configurations']} compared with a typical GW signal. We have chosen the signal predicted in the Higgs portal scenario described in Section \ref{['sec:Hportal']}, with benchmark values $T_*=59.6$, $\alpha=0.17$, $\beta/H_*=12.54$, $\phi_*/T_*=4.07$ (see Table \ref{['table:scalars']}).
• Figure 2: Example of GW spectra in Case 1, for fixed $T_*=100$ GeV, $\alpha=0.5$, $v_w=0.95$, and varying $\beta/H_*$: from left to right, $\beta/H_*=1$ and $\beta/H_*=10$ (top), $\beta/H_*=100$ and $\beta/H_*=1000$ (bottom). The black line denotes the total GW spectrum, the green line the contribution from sound waves, the red line the contribution from MHD turbulence. The shaded areas represent the regions detectable by the C1 (red), C2 (magenta), C3 (blue) and C4 (green) configurations.
• Figure 3: Example of GW spectra in Case 2, for fixed $T_*=100$ GeV, $\alpha=1$, $v_w=1$, $\alpha_\infty=0.3$, and varying $\beta/H_*$: from left to right, $\beta/H_*=1$ and $\beta/H_*=10$ (top), $\beta/H_*=100$ and $\beta/H_*=1000$ (bottom). The black line denotes the total GW spectrum, the blue line the contribution from the scalar field, the green line the contribution from sound waves, the red line the contribution from MHD turbulence. The shaded areas represent the regions detectable by the C1 (red), C2 (magenta), C3 (blue) and C4 (green) configurations.
• Figure 4: Projected eLISA sensitivity to Case 1: non-runaway relativistic bubble walls. Results are displayed for four values of $T_*$ (indicated) and the four eLISA configurations described in Table \ref{['tab:configurations']}. The detectable region is shaded. Also shown are benchmarks from various specific models, discussed in Section \ref{['sec:models']}. All other parameters are as described in the text. Note that the values of $T_*$ chosen correspond only approximately to the precise values for the benchmark points. The GW signal is given primarily by the contribution of sound waves (turbulence is negligible for the chosen value of $\epsilon$).
• Figure 5: Projected eLISA sensitivity to Case 2: runaway bubble walls with finite $\alpha$. Results are displayed for four values of $T_*$ and $\alpha_\infty$ (indicated) and the four eLISA configurations described in Table \ref{['tab:configurations']}. The detectable region is shaded. Also shown are benchmarks from various specific models, discussed in Section \ref{['sec:models']}. All other parameters are as described in the text. Note that the values of $T_*$ and $\alpha_\infty$ chosen correspond only approximately to the precise values for the benchmark points (as described in the text). The GW signal is given primarily by the contribution of the scalar field and of the sound waves.