Gravitational waves from a supercooled electroweak phase transition and their detection with pulsar timing arrays

TL;DR

This work analyzes gravitational-wave production from an electroweak first-order phase transition under extreme supercooling, using a non-linear electroweak realization with a cubic Higgs coupling. It advances beyond the fast-transition paradigm by incorporating cosmic expansion and low-temperature nucleation, finding nucleation around $T_n \sim 50$ GeV and percolation at $T_p$ down to MeV scales. The dominant GW contribution comes from collisions of horizon-scale bubbles, yielding a peak frequency $f_0$ in the $10^{-9}$–$10^{-7}$ Hz range and amplitudes that place the signal at the edge of current PTA exclusions but within SKA sensitivity. This identifies pulsar timing arrays as a promising probe of certain beyond-the-Standard-Model electroweak-phase-transition scenarios.

Abstract

We investigate the properties of a stochastic gravitational wave background produced by a first-order electroweak phase transition in the regime of extreme supercooling. We study a scenario whereby the percolation temperature that signifies the completion of the transition, $T_p$, can be as low as a few MeV (nucleosynthesis temperature), while most of the true vacuum bubbles are formed much earlier at the nucleation temperature, $T_n\sim 50$ GeV. This implies that the gravitational wave spectrum is mainly produced by the collisions of large bubbles and characterised by a large amplitude and a peak frequency as low as $f \sim 10^{-9}-10^{-7}$ Hz. We show that such a scenario can occur in (but not limited to) a model based on a non-linear realisation of the electroweak gauge group, such that the Higgs vacuum configuration is altered by a cubic coupling. In order to carefully quantify the evolution of the phase transition of this model over such a wide temperature range, we go beyond the usual fast transition approximation, taking into account the expansion of the Universe as well as the behaviour of the nucleation probability at low temperatures. Our computation shows that there exists a range of parameters for which the gravitational wave spectrum lies at the edge between the exclusion limits of current pulsar timing array experiments and the detection band of the future Square Kilometre Array observatory.

Figures (3)

• Figure 1: Thermal behaviour of the Euclidean action for $\kappa = -1.9\frac{m_h^2}{v}$. The black solid line corresponds to the action $S(T)$, Eq. (\ref{['eq:S_action']}), whose spacetime dependent bounce solution (\ref{['eq:bounce_general']}) has been solved over a lattice through Newton's method. The blue doted line (resp. red dashed line) is the low (resp high) temperature approximation $S_4(T)$ (resp. $S_3(T)/T$) given by Eq. (\ref{['eq:all_actions']}).
• Figure 2: Thermal evolution of the probability $p(T)$ for $\kappa = [-1.92,-1.87]\frac{m_h^2}{v}$. The intersection between the curves and the red solid line $p(T)=0.7$ gives the percolation temperature.
• Figure 3: Lines: gravitational wave spectra estimated from Eqs. (\ref{['eq:coll']}-\ref{['eq:coll2']}) and the parameters of Table \ref{['tab:alpha_beta']} for $\kappa = [-1.92,-1.88]\frac{m_h^2}{v}$. Green shaded area: current exclusion limits from EPTA vanHaasteren:2011ni. Blue shaded area: planned detection sensitivity of SKA Moore:2014lga.