Confinement Phase Transition From The Early Universe And Its Gravitational Wave Signal

The pure Yang-Mills sector surviving at low energy is of particular interest in the new physics domain.However,if such a theory truly exists in our universe and is sufficiently secluded from the standard model sector,then it is impossible to directly use the high-energy collider for inspection.We can use the gravitational signal from this dark sector in the early universe to test the model.The pure Yang-Mills theory in the dark sector can generate the stochastic gravitational wave background from the confinement phase transition.Therefore,it is necessary to establish a model to describe the confinement phase transition.Due to the non-perturbation structure of pure Yang-Mills theory around the critical temperature,it is challenging to build a model that can correctly and unifiedly account for the deconfinement phase transition and thermodynamics of the hot SU(N)pure Yang-Mills system,for any N.In this paper,three mainstream models used to describe confined phase transition are discussed in detail,and it is found that the Haar measure model,one of the mainstream models,can not describe confinement phase transition and lattice thermodynamic data simultaneously.The reason for it is that Haar type model do not contain transverse gluon.At the same time,the traditional polynomial model,another mainstream model,can not deal with the phase transition except N=3.We using the trick from effective field theory to bulid a modified polynomial model.This modified polynomial model can describe the confinement phase transition and thermodynamics for the color number N≥3 in a self-consistent way,but it can not handle N=2.Moreover,this model can not calculate the bubble wall velocity of the confinement phase transition which is directly related to the gravitational wave signal.To build a unified model for confinement phase transition,in this article,we slightly generalize the massive PYM model to the situation with a quasi gluon mass Mg(T)varying with temperature,inspired by the matrix model.This model will allow as to discuss the nonperturbative confinement phase transition by perturbative model.In such a framework,we can acquire an general effective potential for the temporal gauge field background by perturbative calculation,rather than adding by hand.Under the assumption of unified eigenvalue distribution,we find an simple analytical expression for those general effective potential.The resulting potential works well to describe the behavior of the hot PYM system for all N,via the single parameter Mg(T).Moreover,the Mg(T)fitted by machine learning is found to follow N-universality.Through this model,we find that the statistical pressure which extract from this quasigluon model is similar to a quasi-gluon statistical system that possesses an imaginary chemical potential and this imaginary chemical potential is related to the process that quasi-gluon transformation to other states/particles.Through this information,we can using Boltzmann equation to compute the bubble wall velocity of the confinement phase transition in a selfconsistent way.It is also found that the bubble wall velocities with the color number N=3-8 are all around vw～0.04.We also discussed the bubble dynamics of the confinement phase transition by comparing its pressure with the pressure from the electroweak phase transition.It is found that the process of particles changing from deconfinement vacuum to confinement vacuum can be expressed as the change of imaginary chemical potential.We recalculate the that the gravitational wave signal produced by confined phase transition and it is found that this signal can not be recognized by gravitational wave detectors in the near future.