  We study under which conditions a first-order phase transition in a composite
dark sector can yield an observable stochastic gravitational-wave signal. To
this end, we employ the Linear-Sigma model featuring $N_f=3,4,5$ flavours and
perform a Cornwall-Jackiw-Tomboulis computation also accounting for the effects
of the Polyakov loop. The model allows us to investigate the chiral phase
transition in regimes that can mimic QCD-like theories incorporating in
addition composite dynamics associated with the effects of
confinement-deconfinement phase transition. A further benefit of this approach
is that it allows to study the limit in which the effective interactions are
weak. We show that strong first-order phase transitions occur for weak
effective couplings of the composite sector leading to gravitational-wave
signals potentially detectable at future experimental facilities.
