Dark Temperature Hierarchies and Gravitational Waves from the Electroweak Phase Transition

Abstract

We investigate the impact of a semi-decoupled dark sector with a temperature hierarchy relative to the Standard Model plasma on the electroweak phase transition and its associated gravitational wave signal. Working within a minimal Higgs-portal extension, we allow the dark sector to possess a higher temperature at the electroweak epoch while remaining consistent with cosmological bounds on additional relativistic degrees of freedom. The temperature hierarchy modifies the thermal structure of the effective potential and alters nucleation dynamics without requiring large portal couplings or extreme supercooling. Within the cosmologically allowed window, we find a monotonic enhancement of the gravitational wave amplitude by more than an order of magnitude compared to the standard thermal case, accompanied by a shift of the peak frequency within the millihertz regime. The resulting stochastic background moves substantially closer to the projected sensitivity of future space-based interferometers. Our results demonstrate that hidden-sector temperature hierarchies can leave observable imprints on electroweak-scale phase transitions even in minimal and perturbative frameworks.

Figures (3)

• Figure 1: Dependence of (a) the latent heat parameter $\alpha$ and (b) the inverse duration parameter $\beta/H$ on the dark temperature ratio $\xi=T_D/T$ for $\kappa=1$. Points denote numerical evaluations using the full one-loop effective potential with ring resummation.
• Figure 2: Gravitational wave spectra for $\kappa=1$ and varying dark temperature ratio $\xi=T_D/T$. Increasing $\xi$ enhances the amplitude and shifts the peak toward lower frequencies.
• Figure 3: Signal-to-noise ratio for LISA (four-year mission) as a function of the dark temperature ratio $\xi$ for $\kappa=1$. The shaded region indicates ${\rm SNR} \ge 10$. The vertical dashed line marks the cosmological bound $\xi_{\rm max}=1.8$.