Bubble nucleation and gravitational waves from holography in the probe approximation

We investigate the bounce solution in the holographic dark-QCD and electroweak models with first-order phase transition. The strength parameter α, inverse duration time β/H and bubble wall velocity vw in the gravitational wave power spectra are calculated by holographic bounce solution. We find the parameter α is about 𝒪(1) and β/H is about 104, which implies that the phase transition is fast and strong. The critical temperature, nucleation temperature and the temperature at the beginning time of the phase transition are close to each other in the holographic model. In addition, the velocity vw is found to be less than the sound speed of the plasma cs=1/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {c}_s=1/\sqrt{3} $$\end{document}, which corresponds to the deflagration scenario. The gravitational wave signal from phase transitions is difficult to detect since the factor ϒ suppresses the gravitational wave power spectrum. The GW signal can be detected only when the model is in the period of electroweak phase transition and with suitable parameters. Moreover, the primordial black hole is not favorable for formation due to the large parameter β/H and small velocity vw.