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Hydrodynamic obstruction to bubble expansion

Thomas Konstandin, Jose M. No

TL;DR

The paper identifies a hydrodynamic obstruction to bubble wall acceleration during a cosmological first-order phase transition, arising from heating of the plasma in front of the advancing wall. By analyzing the deflagration regime with a hydrodynamic framework and a bag-like equation of state, it derives a model-dependent, but broadly applicable, criterion relating the critical temperature, nucleation temperature, and latent heat to predict subsonic wall velocities favorable for electroweak baryogenesis. It develops both analytic estimates and a toy model to quantify the obstruction, and discusses how friction interacts with heating to determine the actual wall speed across representative beyond-Standard-Model scenarios. The results imply that subsonic walls—and thus viable baryogenesis—may be more robust to friction than previously thought, provided the heating-induced obstruction condition is satisfied. This has implications for the viability of electroweak baryogenesis in MSSM-like and singlet-extended models and informs predictions for gravitational wave signals and cosmological relics from bubble dynamics.

Abstract

We discuss a hydrodynamic obstruction to bubble wall acceleration during a cosmological first-order phase transition. The obstruction results from the heating of the plasma in the compression wave in front of the phase transition boundary. We provide a simple criterion for the occurrence of the obstruction at subsonic bubble wall velocity in terms of the critical temperature, the phase transition temperature, and the latent heat of the model under consideration. The criterion serves as a sufficient condition of subsonic bubble wall velocities as required by electroweak baryogenesis.

Hydrodynamic obstruction to bubble expansion

TL;DR

The paper identifies a hydrodynamic obstruction to bubble wall acceleration during a cosmological first-order phase transition, arising from heating of the plasma in front of the advancing wall. By analyzing the deflagration regime with a hydrodynamic framework and a bag-like equation of state, it derives a model-dependent, but broadly applicable, criterion relating the critical temperature, nucleation temperature, and latent heat to predict subsonic wall velocities favorable for electroweak baryogenesis. It develops both analytic estimates and a toy model to quantify the obstruction, and discusses how friction interacts with heating to determine the actual wall speed across representative beyond-Standard-Model scenarios. The results imply that subsonic walls—and thus viable baryogenesis—may be more robust to friction than previously thought, provided the heating-induced obstruction condition is satisfied. This has implications for the viability of electroweak baryogenesis in MSSM-like and singlet-extended models and informs predictions for gravitational wave signals and cosmological relics from bubble dynamics.

Abstract

We discuss a hydrodynamic obstruction to bubble wall acceleration during a cosmological first-order phase transition. The obstruction results from the heating of the plasma in the compression wave in front of the phase transition boundary. We provide a simple criterion for the occurrence of the obstruction at subsonic bubble wall velocity in terms of the critical temperature, the phase transition temperature, and the latent heat of the model under consideration. The criterion serves as a sufficient condition of subsonic bubble wall velocities as required by electroweak baryogenesis.

Paper Structure

This paper contains 8 sections, 75 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Origin of the obstruction
  3. The heating effect
  4. Local equations of motion in a toy model
  5. Solving the local equations of motion
  6. A concrete (toy) model
  7. Friction revisited
  8. Discussion

Figures (4)

  • Figure 1: Example for a deflagration. The left plot shows the fluid velocity $v(\xi)$ while the right plot shows the enthalpy $w(\xi)$.
  • Figure 2: The heating effect assuming a wall velocity of the speed of sound, $\xi_w=c_s$. The plot shows $\log T_+/T_N$ as a function $\alpha_+$. The dashed line is the leading order result (\ref{['eq:ToT_leading']}) while the straight line is the fit (\ref{['eq:ToT_fit']}) to the numerical result.
  • Figure 3: The wall velocity of the obstruction versus $\phi_c/T_c$ for the values $T_c=0.6$, $T_c=0.9$, and $T_c=1.5$. The Higgs mass is $m_H = 120$ GeV and the gray bands correspond to the estimate in (\ref{['eq:estv3']}).
  • Figure 4: The heating effect assuming a wall velocity of the speed of sound, $\xi_w=c_s$. The plot displays the relation between the parameters of the phase transition at critical temperature in relation to the parameters in front of the phase boundary in the toy model (\ref{['eq:Vtoy']}).