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.

Context. Abundances of beryllium in metal-poor stars scale linearly with metallicity down to [Fe/H] ∼ −3.0. In the stars where Be has been detected at this extremely metal-poor regime, an increased abundance scatter has been previously reported in the literature. This scatter could indicate a flattening of the relation between Be abundances and metallicity. Aims. Our aim is to perform a new investigation of Be abundances in extremely metal-poor stars and try to clarify whether a Be abundance plateau exists. We revisited the Be abundances in a sample of nine dwarfs with metallicities close to [Fe/H] ∼ −3.0. Additionally, we analysed the Be lines in the spectra of stars BPS BS 16968-0061 and CD-33 1173 for the first time. Methods. We took advantage of Gaia DR2 parallaxes to refine values of the surface gravity of the stars. Updated values of surface gravity can have a significant impact on the determination of Be abundances. The other atmospheric parameters were computed using photometric and spectroscopic data. Abundances of Be were determined using spectrum synthesis and model atmospheres. Results. Some of the stars indeed suggest a flattening. Over about a 0.5 dex range in metallicity, between [Fe/H] ∼ −2.70 and −3.26, the Be abundances stay mostly constant at about log(Be/H) ∼ −13.2 dex. Nevertheless, for several stars, we could only place upper limits that are below that level. Most of the sample stars are consistent with having been formed at the progenitor of the so-called Gaia-Enceladus merger. Two out of the three stars likely formed in-situ are the ones that deviate the most from the linear relation. Conclusions. The mixed origin of these extremely metal-poor stars offers a clue to understanding the flattening. We suggest that our observations can be naturally understood as a consequence of the inhomogeneous star forming conditions in the early Galaxy. Without efficient mixing, the early interstellar medium would be characterised by a large scatter in Fe abundances at a given moment. Beryllium, on the other hand, because of its origins in cosmic-ray spallation, would have more homogeneous abundances (in a Galaxy-wide sense). We therefore suggest that the observed flattening of the Be-versus-metallicity relation reflects a stronger scatter in the Galactic Fe abundances at a given age.

We study the possible gravitational wave signal and the viability of baryogenesis arising from the electroweak phase transition in an extension of the Standard Model (SM) by a scalar singlet field without a ℤ2 symmetry. We first analyze the velocity of the expanding true-vacuum bubbles during the phase transition, confirming our previous finding in the unbroken ℤ2 symmetry scenario, where the bubble wall velocity can be computed from first principles only for weak transitions with strength parameters α ≲ 0.05, and the Chapman-Jouguet velocity defines the maximum velocity for which the wall is stopped by the friction from the plasma. We further provide an analytical approximation to the wall velocity in the general scalar singlet scenario without ℤ2 symmetry and test it against the results of a detailed calculation, finding good agreement. We show that in the singlet scenario with a spontaneously broken ℤ2 symmetry, the phase transition is always weak and we see no hope for baryogenesis. In contrast, in the case with explicit ℤ2 breaking there is a region of the parameter space producing a promising baryon yield in the presence of CP violating interactions via an effective operator involving the singlet scalar and the SM top quarks. Yet, we find that this region yields unobservable gravitational waves. Finally, we show that the promising region for baryogenesis in this model may be fully tested by direct searches for singlet-like scalars in di-boson final states at the HL-LHC, combined with present and future measurements of the electron electric dipole moment.

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