Various observations from particle physics, astrophysics, and cosmology have suggested that the standard model of particle physics for describing the microscopic structure of matter is not complete. It is then one of the vital scientific problems of current particle physics and cosmological observations to search for the signals of new physics beyond the standard model of particle physics. Many new physics models beyond the standard model of particle physics predict the cosmological first-order phase transitions during the evolution of our Universe. With the temperature decreasing due to the expansion of the Universe, symmetries at high energy scales would be broken simultaneously, and the associated quantum field would decay into the true vacuum from the false vacuum by quantum tunneling via the nucleation and expansion of true-vacuum bubbles, resulting in the energy transfer into the kinetic energy of bubble walls and background fluid, similar to the violent process of frozen ice from supercooling water. The following collisions among expanding bubbles would induce large fluctuations in the energy density. Therefore, as a violent process in the early Universe, the cosmological first-order phase transitions could produce various observational effects, including the stochastic gravitational wave background, primordial magnetic field, and baryon asymmetry, making it feasible to probe or constrain the new physics from astrophysical and cosmological observations. The gravitational-wave observation from cosmological first-order phase transition is also one of the main scientific targets of many gravitational-wave observational projects.

Recently, the postdoc Dr. Jing Liu from the International Centre for Theoretical Physics Asia-Pacific of the University of Chinese Academy of Sciences, the associate researcher Prof. Ligong Bian from Chongqing University, the researchers Prof. Rong-Gen Cai, Prof. Zong-Kuan Guo, and the postdoc Dr. Shao-Jiang Wang from the Institute of Theoretical Physics of Chinese Academy of Sciences have proposed a new mechanism for the productions of primordial black holes, and given rise to rigorous constraints on the properties of cosmological first-order phase transitions from the astrophysical observational data. Due to the randomness of quantum tunneling, the progress of vacuum decay varies in different regions. Note that the false vacuum energy density barely changes with the cosmological expansion, while the energy densities of other matter components like radiations and cold dark matter are rapidly diluted with the expansion of the Universe. Therefore, the regions of vacuum decay that fall behind the others would admit higher energy densities after the phase transition. This is to say that the cosmological first-order phase transition would induce fluctuations in energy density. These high-energy-density regions would eventually produce primordial black holes via gravitational collapse, and these primordial black holes are almost monochromatic in their mass spectrum. The relevant paper has been published as a Letter in Phys. Rev.D 105 (2022) L021303. The primordial black holes produced with this mechanism and the associated gravitational waves could explain the merger rate of black hole binaries observed in LIGO-Virgo collaborations as well as the signal from the NANOGrav observation.

They also discovered that the first-order phase transition could induce superhorizon curvature perturbations, and in turn probe and constrain the phase-transition properties from the observations of the curvature perturbations at small cosmological scales. The nucleation rate of true vacuum bubbles per unit time and per unit volume could be obtained from the quantum tunneling. After the phase transition, the regions with a scale larger than the product of phase-transition duration and light speed share no causal connection, and the causality requires the energy density spectrum of curvature perturbations to be proportional to the cube of wavenumber. Hence, if the superhorizon scale is considered, the induced curvature perturbations from phase transitions could largely surpass the primordial perturbations from the early-universe inflation so that it can be probed by various astrophysical observations, including the temperature anisotropies and spectrum distortion in the cosmic microwave background radiations and the number density in ultra-compact minihalos. In turn, we could also constrain the phase-transition properties via the upper bounds on the curvature perturbations from these astrophysical observations.

*Figure 1: Constraints on the parameter space of phase transition from different observations on the curvature perturbations, where alpha denotes the phase-transition strength, beta/H_* denotes the phase-transition rate, and T_* is the phase-transition temperature. The gray solid curves and gray dotted curves in the left and middle panels are constraints from the gravitational-wave background and big bang nucleosynthesis, respectively.*

They have obtained the power spectrum of the curvature perturbations induced from the first-order phase transitions, and for the first time given rise to rigorous constraints on the phase-transition parameters from the upper bounds on the curvature perturbations from astrophysical observations. The relevant paper has been published in Phys. Rev. Lett 130 (2023) 051001. As shown in Figure 1, all constraints on the cosmological first-order phase transitions below the electroweak scale are obtained from the upper bounds on the curvature perturbations from the big bang nucleosynthesis (blue curves), the temperature anisotropies and spectrum distortion in the cosmic microwave background radiations (green curves), and the number density in ultra-compact minihalos (orange solid curves from pulsar timing array and orange dashed curves from Gamma-ray detections). This study largely enhances the previous constraints from the stochastic gravitational-wave background (gray solid curves) and big bang nucleosynthesis (gray dotted curves) on the QCD first-order phase transition, low-energy dark-sector first-order phase transition, and some of the electroweak first-order phase transition, in particular the low-energy transitions and slow first-order phase transitions.

This study is supported by relevant projects from the National Natural Science Foundation of China, the Ministry of Science and Technology of China, and the Chinese Academy of Sciences.

**Link: **

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.051001

**Contact:**

Jing Liu: liujing@ucas.ac.cn

International Centre for Theoretical Physics Asia-Pacific