Bubble nucleation and gravitational wave from holography

Abstract: We investigate the bounce solution in the holographic QCD and electroweak models with first-order phase transition. The strength parameter $\alpha$, inverse duration time $\beta/H$, and bubble wall velocity $v_w$ in the gravitational wave power spectra are calculated by holographic bounce solution. In contrast to the results of field theory, we find the parameter $\alpha$ is about $\mathcal{O}(1)$ and $\beta/H$ is about $10^4$, which imply that the phase transition is fast and strong. The critical, nucleation and percolation temperatures of the phase transition are close to each other in the holographic model. In addition, the velocity $v_w$ is found to be less than the sound speed of the plasma $c_{s}=1/\sqrt{3}$, which corresponds to the deflagration scenario. For QCD phase transition, the gravitational wave power spectrum can reach $10^{-13}-10^{-14}$ around the peak frequency of 0.01 Hz, which can be detected by BBO and Ultimate-DECIGO. For electroweak phase transition, the gravitational wave power spectrum can reach $10^{-12}-10^{-16}$ around the peak frequency $1-10$ Hz. Moreover, the primordial black hole is not favorable for formation due to the large parameter $\beta/H$ and small velocity $v_w$.