  Within classically conformal models, the spontaneous breaking of scale
invariance is usually associated to a strong first order phase transition that
results in a gravitational wave background within the reach of future
space-based interferometers. In this paper we study the case of the classically
conformal gauged B-L model, analysing the impact of this minimal extension of
the Standard Model on the dynamics of the electroweak symmetry breaking and
derive its gravitational wave signature. Particular attention is paid to the
problem of vacuum stability and to the role of the QCD phase transition, which
we prove responsible for concluding the symmetry breaking transition in part of
the considered parameter space. Finally, we calculate the gravitational wave
signal emitted in the process, finding that a large part of the parameter space
of the model can be probed by LISA.
