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The detection of stochastic background of gravitational waves (GWs), producedby cosmological phase transitions (PTs), is of fundamental importance becauseallows to probe the physics related to PT energy scales. Motivated by thedecisive role of non-zero quark chemical potential towards understandingphysics in the core of neutron stars, quark stars and heavy-ion collisions, inthis paper we qualitatively explore the stochastic background of GW spectrumgenerated by a cosmological source such as high-density QCD first order PTduring 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 chiralquarks 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 toimprove the chances of detection, in possible future observations (inparticular SKA/PTA experiments), of the stochastic background of GWs from QCDfirst order PT. Even if the improvements could be weak, by updating thesensitivity of relevant detectors in the future, we can still remain hopeful.Concerning the phenomenological contribution of QCD equation-of-state, and inparticular the possibility to detect a stochastic GW signal, we further showthat the role of the quark chemical potential is model-dependent. This featureallows to discriminate among possible QCD effective models depending on theircapability to shed light on the dynamic of QCD-PT through future observationsof primordial GWs. In this perspective, the results are indeed encouraging toemploy the GWs to study the QCD PT in high density strong interaction matter.

The quark chemical potential of QCD phase transition and the stochastic background of gravitational waves