Electroweak Bubble Wall Speed Limit (1703.08215v2)

Abstract: In extensions of the Standard Model with extra scalars, the electroweak phase transition can be very strong, and the bubble walls can be highly relativistic. We revisit our previous argument that electroweak bubble walls can "run away," that is, achieve extreme ultrarelativistic velocities $\gamma \sim 10^{14}$. We show that, when particles cross the bubble wall, they can emit transition radiation. Wall-frame soft processes, though suppressed by a power of the coupling $\alpha$, have a significance enhanced by the $\gamma$-factor of the wall, limiting wall velocities to $\gamma \sim 1/\alpha$. Though the bubble walls can move at almost the speed of light, they carry an infinitesimal share of the plasma's energy.

• The paper demonstrates that runaway bubble wall speeds are halted by transition radiation, which increases friction through soft gauge boson emission.
• The analysis establishes that bubble wall speeds are capped near γ ~ 1/α, influencing the conditions for baryogenesis and the generation of gravitational waves.
• The study utilizes extensions to the Standard Model with extra scalar fields to refine the understanding of first-order electroweak phase transitions and their dynamics.

Electroweak Bubble Wall Speed Limit

The research presented in this paper discusses the velocity dynamics of bubble walls formed during the first-order electroweak phase transition, a stage in the Universe's early expansion. The primary focus lies on the speed at which these bubble walls expand into the high-temperature plasma. Specifically, the paper revisits the hypothesis that bubble walls could achieve extremely high ultrarelativistic velocities, which the authors refer to as "runaway" velocities. However, they show that such runaway behavior is not ubiquitous, identifying limits on bubble wall speeds due to transition radiation.

Summary of Key Findings

In the context of extensions to the Standard Model that include extra scalar fields, the strength of the electroweak phase transition is significantly enhanced. Previous arguments suggested that these conditions foster scenarios where bubble walls could potentially "run away," achieving gamma factors on the order of $\gamma \sim 10^{14}$. The paper invalidates this claim by introducing the effect of transition radiation, a mechanism akin to transition radiation observed when particles move between media with different electromagnetic properties.

The paper elucidates how particles crossing the wall emit transition radiation, emitted soft gauge bosons, which substantially increase the friction experienced by the bubble wall. This friction, primarily a consequence of phase-dependent mass adjustments of gauge bosons like the W and Z, grows linearly with the gamma factor, eventually providing a self-limiting mechanism to the acceleration of the bubble wall. The analysis shows that while bubble walls can approach relativistic speeds near the speed of light, they will not achieve runaway velocities indefinitely, with a velocity limit typically around $\gamma \sim 1/\alpha$ due to this transition radiation, where $\alpha$ represents the gauge coupling constant.

Implications and Future Considerations

The refined understanding of bubble wall velocity has profound implications for theoretical predictions concerning baryogenesis and gravitational wave signatures from the early Universe. The wall dynamics influence the conditions under which baryon asymmetry could be generated, particularly through variations of the Sakharov conditions at high wall velocities. Moreover, the accurate characterization of these dynamics is crucial for interpreting data from gravitational wave experiments, as wall movement affects the resulting gravitational waves emitted during the phase transition.

Theoretically, the findings underscore the importance of considering higher-order radiative processes and interaction dynamics in field-theoretic and phenomenological models of phase transitions, especially those incorporating beyond the Standard Model physics. Practically, understanding the electroweak phase transition better couple with precision measurements from upcoming experimental probes of the early Universe, such as those from the cosmic microwave background or next-generation colliders, to place constraints on new scalar fields and the possible strength of such transitions.

Future work should delve into the quantitative evaluation of soft emission and saturation limits within specific models, explore nonperturbative effects arising from high-densities of emitted gauge bosons, and the post-wall dynamics, particularly regarding implications for the re-thermalization processes and induced sphaleron transitions. Such studies could push the frontier in electroweak baryogenesis and further our grasp of the Universe's thermal history.