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

## TL;DR

This paper explores the gravitational wave background generated by a supercooled electroweak phase transition, highlighting the potential for detection by pulsar timing arrays and the impact of extreme supercooling on the spectrum.

## Contribution

It introduces a detailed analysis of gravitational waves from a supercooled electroweak phase transition, including a model with a cubic Higgs coupling and a comprehensive treatment of the transition dynamics.

## Key findings

- Gravitational wave spectrum peaks at very low frequencies (~10^{-9}-10^{-7} Hz).
- Certain parameter ranges make the spectrum detectable by future pulsar timing arrays.
- The scenario can occur in models with a non-linear realization of the electroweak gauge group.

## 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.