Can electroweak bubble walls run away? (0903.4099v3)

Abstract: In extensions of the Standard Model with SU(2) singlet scalar fields, there can be regions of parameter space for which the electroweak phase transition is first order already at the mean-field level of analysis. We show that in this case the phase interface (bubble wall) can become ultra-relativistic, with the relativistic gamma factor gamma = (1-v_{wall}^2)^{-1/2} growing linearly with the wall's propagation distance. We provide a simple criterion for determining whether the bubble wall "runs away" in this way or if gamma approaches a terminal value.

• The paper derives a criterion to determine when electroweak bubble walls can run away, resulting in a gamma factor that grows with distance.
• It shows that runaway behavior occurs in models with a mean-field first-order transition, while fluctuation-induced transitions do not support it.
• Implications include the generation of strong gravitational wave signals and enhanced prospects for electroweak baryogenesis in extended Standard Model scenarios.

Can Electroweak Bubble Walls Run Away?

The paper "Can electroweak bubble walls run away?" by Dietrich B\"odeker and Guy D. Moore investigates the dynamics of bubble walls in the context of a first-order electroweak phase transition, a phenomenon that can occur in certain extensions of the Standard Model (SM). Their analysis specifically focuses on the conditions under which bubble walls may achieve ultra-relativistic speeds, or "run away," during the phase transition.

Background and Motivation

In extensions of the Standard Model, particularly those introducing SU(2) singlet scalar fields, the electroweak phase transition can be first order. This characteristic is cosmologically significant as it can give rise to scenarios such as electroweak baryogenesis, primordial magnetic fields, and detectable gravitational wave backgrounds. These scenarios crucially depend on the strength of the electroweak phase transition and the velocity of the bubble walls during the transition.

Key Findings and Results

The authors derive a criterion to determine whether the bubble wall "runs away" with a gamma factor ($\gamma$) increasing linearly with propagation distance or if $\gamma$ approaches a terminal value. They conclude that runaway behavior is possible in models that exhibit a first-order transition at the mean-field level, such as those with SU(2) singlet scalars. However, they demonstrate that in the absence of a mean-field first-order transition, or when the transition is fluctuation-induced, runaway walls are not expected.

Theoretical Insights:

• The effective potential ($V$) is analyzed as a function of temperature, with contributions from the vacuum and thermal parts. The interplay between the two determines the phase dynamics.
• At ultra-relativistic speeds, the friction on the bubble wall is determined by modifying the thermal potential using mean-field approximations.
• The authors scrutinize under what thermodynamic conditions such walls could propagate with non-subsonic velocities, addressing both energy and entropy changes across the phase interface.

Practical and Theoretical Implications

The findings of this paper have various practical implications for theoretical physics and cosmology:

• Baryogenesis: The velocity of bubble walls impacts the efficiency of baryon number generation in the early universe. Slow wall velocities may favor baryon number preservation due to nonequilibrium conditions in the symmetric phase.
• Gravitational Waves: Runaway bubble walls, with a large gamma factor, may be responsible for generating strong gravitational wave signals during phase transitions, which are pertinent to current and future experiments such as LIGO and LISA.
• Parameter Space of New Theories: This work offers a criterion for model builders to evaluate which theoretical extensions of the Standard Model might exhibit interesting cosmological dynamics.

Future Directions

Speculation on future directions includes considering more complex models like the Next-to-Minimal Supersymmetric Standard Model (nMSSM) and addressing loop corrections beyond one-loop level to refine predictions. There is also an opportunity to explore the implications for alternative cosmological scenarios that might not strictly be tied to electroweak physics but involve similar phase transition dynamics.

Overall, the paper provides a rigorous examination of the dynamics of electroweak bubble walls, offering a comprehensive criterion to discern their propagation characteristics, thus contributing to our understanding of early universe cosmology and particle physics beyond the Standard Model.