Abstract
Computing the properties of the bubble wall of a cosmological first order phase transition at electroweak scale is of paramount importance for the correct prediction of the baryon asymmetry of the universe and the spectrum of gravitational waves. By means of the semiclassical formalism we calculate the velocity and thickness of the wall using as theoretical framework the scalar singlet extension of the SM with a parity symmetry and the SM effective field theory supplemented by a dimension six operator. We use these solutions to carefully predict the baryon asymmetry and the gravitational wave signals. The singlet scenario can easily accommodate the observed asymmetry but these solutions do not lead to observable effects at future gravity wave experiments. In contrast the effective field theory fails at explaining the baryon abundance due to the strict constraints from electric dipole moment experiments, however, the strongest solutions we found fall within the sensitivity of the LISA experiment. We provide a simple analytical approximation for the wall velocity which only requires calculation of the strength and temperature of the transition and works reasonably well in all models tested. We find that generically the weak transitions where the fluid approximation can be used to calculate the wall velocity and verify baryogenesis produce signals too weak to be observed in future gravitational wave experiments. Thus, we infer that GW signals produced by simple SM extensions visible in future experiments are likely to only result from strong transitions described by detonations with highly relativistic wall velocities.
Highlights
First order transitions are characterized by the nucleation of bubbles of a symmetry breaking vacuum phase [76,77,78] which subsequently expand and eventually collide ending the transition
In contrast the effective field theory fails at explaining the baryon abundance due to the strict constraints from electric dipole moment experiments, the strongest solutions we found fall within the sensitivity of the LISA experiment
We find that generically the weak transitions where the fluid approximation can be used to calculate the wall velocity and verify baryogenesis produce signals too weak to be observed in future gravitational wave experiments
Summary
First-order phase transitions proceed via nucleation of bubbles of broken phase in the space filled with unstable phase. This nucleation criteria has to be modified and in the most serious calculations one needs to include the vacuum contribution in the Hubble parameter and compute the temperature of percolation It is usually assumed, that first-order phase transitions are instant and complete at the temperature T ≈ Tn. all the parameters determining gravitational-wave signal are typically evaluated at this value. A complete solution would require an iterative method which we consider a level of diligence and we will leave this issue as beyond the scope of this paper Due to this complication our estimation for the wall velocity will be performed at the nucleation temperature, obtained from the condition S3/Tn ≈ 140. The parameters β and α introduced above and the bubble wall-velocity play a central role in determining the GW spectrum which will be discussed in a subsequent section
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