Stochastic gravitational waves produced by the first-order QCD phase transition

Abstract: We investigate the stochastic gravitational waves background arising from the first-order QCD chiral phase transition, considering three distinct sources: bubble collisions, sound waves, and fluid turbulence. Within the framework of the Polyakov-Nambu-Jona-Lasinio (PNJL) model, we calculate the parameters governing the intensity of the gravitational wave phase transition and determine their magnitudes along the adiabatic evolutionary path. We introduce the effective bag constant $B_{\mathrm{eff}}$ related to the dynamical evolution of quarks to evaluate the intensity of the phase transition. By calculating expanded potential at the point of false vacuum, we find that all the bubbles are in the mode of runaway, leading the velocity of the bubble wall to the speed of light. The resulting gravitational wave energy spectrum is estimated, revealing a characteristic amplitude of the generated gravitational waves within the centihertz frequency range. We present the gravitational wave spectrum and compare it with the sensitivity range of detectors, and find that the gravitational wave spectra generated by these sources have the potential to be detected by future detectors such as BBO and $\mu$ARES.