Gravitational waves and primordial black holes from chirality imbalanced QCD first-order phase transition with $\mathcal {P}$ and $\mathcal {CP}$ violation

TL;DR

This paper investigates how a first-order QCD phase transition with nd P violation, induced by chirality imbalance, can produce detectable gravitational waves and primordial black holes, considering effects of magnetic fields and transition dynamics.

Contribution

It presents a novel analysis of gravitational wave spectra and primordial black hole formation from a chirality imbalance-driven first-order QCD phase transition with nd P violation, including magnetic field effects.

Findings

Gravitational waves from this transition could be detected by LISA, Taiji, and DECIGO.

The phase transition has a very high inverse duration /H, around 10^4.

Primordial black hole formation is unlikely due to rapid phase transition completion.

Abstract

The chirality imbalance in QCD is spontaneously induced by a repulsive axial-vector interaction from the instanton anti-instanton pairing at high temperature above the chiral phase transition, and vanishes at low temperature. The chiral chemical potential $\mu_5$ is in the same magnitude as estimated from the sphaleron transition. Phase transition of the chirality imbalance is always a first-order one in the early universe with $\mathcal {P}$ and $\mathcal {CP}$ violation. The spectra of gravitational waves and the formation of the primordial black holes from this first-order phase transition is investigated in this work, and the effect of a strong magnetic field is also analyzed. The gravitational waves produced by chirality imbalance can be detected by LISA, Taiji and DECIGO, with the peak energy density locating in the range of $10^{-11}$ to $10^{-9}$ and the peak frequencies lying in the range of $10^{-5}$ Hz to $10^{-2}$ Hz. The spectrum with larger axial vector coupling strength and stronger magnetic field has higher peak energy density and lower peak frequency. According to this trend, the gravitational waves spectra might also be able to be detected by SKA, IPTA and EPTA. The Phase transition inverse duration $\beta/H_*$ calculated from the bounce solution is in the order of $10^4$, which is much higher than typical value $10-100$ from electroweak phase transitions. Based on the mechanism of postponement of the false vacuum decay, it is found that the formation of the primordial black hole is not favored because the phase transition completes in an extreme short time due to the large value of $\beta/H_*$ and thus the false vacuum energy density decays sharply.