  The detection of stochastic background of gravitational waves (GWs), produced
by cosmological phase transitions (PTs), is of fundamental importance because
allows to probe the physics related to PT energy scales. Motivated by the
decisive role of non-zero quark chemical potential towards understanding
physics in the core of neutron stars, quark stars and heavy-ion collisions, in
this paper we qualitatively explore the stochastic background of GW spectrum
generated by a cosmological source such as high-density QCD first order PT
during the early Universe. Specifically, we calculate the frequency peak
$f_{peak}$ redshifted at today time and the fractional energy density
$\Omega_{gw}h^2$ in light of equation-of-state improved by the finite quark
(baryon) chemical potential (we consider an effective three flavor chiral
quarks model of QCD). Our calculations reveal a striking increase in $f_{peak}$
and $\Omega_{gw}h^2$ due to the quark chemical potential, which means to
improve the chances of detection, in possible future observations (in
particular SKA/PTA experiments), of the stochastic background of GWs from QCD
first order PT. Even if the improvements could be weak, by updating the
sensitivity of relevant detectors in the future, we can still remain hopeful.
Concerning the phenomenological contribution of QCD equation-of-state, and in
particular the possibility to detect a stochastic GW signal, we further show
that the role of the quark chemical potential is model-dependent. This feature
allows to discriminate among possible QCD effective models depending on their
capability to shed light on the dynamic of QCD-PT through future observations
of primordial GWs. In this perspective, the results are indeed encouraging to
employ the GWs to study the QCD PT in high density strong interaction matter.
