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

Abstract

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 Ωgwh 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 Ωgwh 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.

Unveiling the gravitational universe at μ-Hz frequencies

“…Since the frequency range of PTA observatories corresponds to k ∼ H * at the energy scale T * = 100 MeV (see (1)), PTA can only probe very slow QCD PTs featuring β/H * of O(1) or smaller. A weaker and briefer first order PT instead seems more likely [36,62,103,170]. A detector operating in the μ-Hz range would vastly improve our capability to investigate the cosmological QCD PT, as it would be sensitive to much wider regions of the PT parameter space, covering 10 β/H * 10 9 .…”

Gravitational Waves from the Cosmological Quark-Hadron Phase Transition Revisited

“…For temperatures higher than T χ the quark condensate vanishes and the symmetry is restored. Equations of state based on chiral models are also associated to non-null quark chemical potentials (see, for instance [10][11][12] and references therein), incorporating as well an external pion field. The properties of the QCD transition have also been derived from the Hawking-Page phase transition by using the AdS/QCD correspondence and, in particular, the duration of the transition was assumed to be equal to the evaporation timescale of the equivalent five-dimensional AdS black hole [13,14].…”

Minimal length, maximal momentum and stochastic gravitational waves spectrum generated from cosmological QCD phase transition

“…It is known that there is still no sure way to find κ. Since, the roles of parameters α and κ are very important on the definitions of peak position and the SGW signal's amplitude, we use β = nH * , n = 5 and 10, µ = 0.7 and κ b ǫ 1+ǫ = κmǫ 1+ǫ = 0.05 [21,22]. According to the general relation between Hubble parameter and the energy density, the Hubble parameter at transition epoch can be defined as…”

“…It acquires a modification since the interaction measure is marked by the trace anomaly that is expected to lead to some exciting cosmic results such as the prediction of Weakly Interacting Massive Particles (WIMPs), and pure glue lattice QCD calculations [20]. Some interesting investigations are in progress in this direction [21,22]. Trace anomaly has been considered solemnly in [21], energy density is computed from trace anomaly to deduce the equation of state that emerged from parametrization of the pressure due to u, d, and s quarks and the gluons.…”

“…The remarkable differences that have been noticed there is that the rate of expansion of the universe is decreased, however, the gravitational wave signal is increased by almost 50% with a redshift of the peak frequency to the current time by 25%. In [22], a fractional energy density and redshift of the peak frequency at the current time of SGW is investigated using an effective QCD equation of state of three quark flavors u, d, and s including chemical potential taking finite temperature effect into account where it is found that the frequency and amplitude of SGW signal present today, get enhanced with an increase in the chemical potential.…”