Affleck-Dine baryogenesis generated high baryon density in the early Universe. The baryon chemical potential enhanced the potential barrier and significantly reduced the decay rate of false vacuum, which decreased from infinity at the critical end point to zero at the critical nucleation point. When the decay rate reached zero, the false vacuum of high baryon density quark matter was unlikely to decay and could persist over cosmological time scales. Therefore, primordial quark nuggets (PQNs) could form and survive in the early Universe as the seeds of compact stars. This new mechanism for the formation of PQNs is different from Witten's stable droplet of quark matter.

China

Jingdong Shao

Hong Mao

Mei Huang

Nanohertz gravitational waves and primordial quark nuggets from dense QCD matter in the early Universe * Supported in part by the National Natural Science Foundation of China (12235016, 12221005), and the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030000)

<p>We investigate the gravitational wave spectrum induced by first-order quantum chromodynamics (QCD) phase transitions, e.g., the confinement-deconfinement phase transition of the pure gluon system and the chiral phase transitions in the quark-meson model and Polyakov quark-meson model. The gravitational wave power spectra are sensitive to the phase transition rate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi><mo>/</mo><mi>H</mi></math>. All QCD models predict a relatively large phase transition rate in the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi><mo>/</mo><mi>H</mi><mo>∼</mo><msup><mn>10</mn><mn>4</mn></msup></math> at high temperature region, and the produced gravitational waves lie in the peak frequency region of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mi>–</mi><mn>0.01</mn><mtext> </mtext><mtext> </mtext><mi>Hz</mi></mrow></math>, corresponding to an energy spectrum in the range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>8</mn></mrow></msup><mi>–</mi><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup></mrow></math>, which can be detected by LISA and Taiji. If a high baryon density region is generated through Affleck-Dine baryogenesis or other mechanisms, the baryon chemical potential significantly reduces the phase transition rate, which will drop to the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi><mo>/</mo><mi>H</mi><mo>∼</mo><msup><mn>10</mn><mn>1</mn></msup></math>, thus leading to the production of nanohertz gravitational waves. Furthermore, there exists a critical quark chemical potential with zero phase transition rate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi><mo>/</mo><mi>H</mi><mo>=</mo><mn>0</mn></math>, indicating that the false vacuum will not decay, which supports the formation of primordial quark nuggets in the early Universe.</p>

Transition rate and gravitational wave spectrum from first-order QCD phase transitions

By using the analytic continuation method, a polarized Polykov-loop potential at finite real angular velocity is constructed from the lattice results at finite imaginary angular velocity. The chiral and deconfinement phase transitions under rotation have been simultaneously investigated in the polarized-Polyakov-loop Nambu–Jona-Lasinio (PPNJL) model. It is observed that both critical temperatures of deconfinement and chiral phase transition increase with the angular velocity, which is in consistent with lattice results. The spin alignment of vector meson has the negative deviation of <math><msub><mi>ρ</mi><mn>00</mn></msub><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></math> under rotation, and the deviation in the PPNJL model is much more significant than that in the NJL model and the quark coalescence model, which revealing the important role of rotating gluons on the quark polarization.

Fei Sun

Rui Wen

Kun Xu

Chiral phase transition and spin alignment of vector mesons in the polarized-Polyakov-loop Nambu–Jona-Lasinio model under rotation

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 <math><msub><mi>μ</mi><mn>5</mn></msub></math> 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 <math><mi>P</mi></math> and <math><mrow><mi>C</mi><mi>P</mi></mrow></math> 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 <math><msup><mn>10</mn><mrow><mo>−</mo><mn>11</mn></mrow></msup></math> to <math><msup><mn>10</mn><mrow><mo>−</mo><mn>9</mn></mrow></msup></math> and the peak frequencies lying in the range of <math><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>Hz</mi></math> to <math><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>Hz</mi></math>. 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 <math><mi>β</mi><mo>/</mo><msub><mi>H</mi><mo>*</mo></msub></math> calculated from the bounce solution is in the order of <math><msup><mn>10</mn><mn>4</mn></msup></math>, 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 <math><mi>β</mi><mo>/</mo><mi>H</mi><mo>*</mo></math> and thus the false vacuum energy density decays sharply.

Gravitational waves and primordial black holes from chirality imbalanced QCD first-order phase transition with <math><mrow><mi>P</mi></mrow></math> and <math><mrow><mi>C</mi><mi>P</mi></mrow></math> violation