The Scalar Singlet Extension of the Standard Model: Gravitational Waves versus Baryogenesis

Understand

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 $\mathbb{Z}_2$ symmetry.

• We first analyze the velocity of the expanding true-vacuum bubbles during the phase transition, confirming our previous finding in the unbroken $\mathbb{Z}_2$ symmetry scenario, where the bubble wall velocity can be computed from first principles only for weak transitions with strength parameters $\alpha \lesssim 0.05$, 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 $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ symmetry, the phase transition is always weak and we see no hope for baryogenesis.