  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.
