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Bubble wall velocity: heavy physics effects

Aleksandr Azatov, Miguel Vanvlasselaer

TL;DR

The paper analyzes the dynamics of relativistic bubble expansion during first-order phase transitions in the ultra-relativistic regime (γ ≫ 1). It demonstrates that heavy fields, even if decoupled at the transition scale, can impart significant friction on the bubble wall, potentially preventing runaway expansion, using a two-scalar toy model and a mixing mechanism. It reviews NLO friction arising from soft vector-boson emission, presenting an equivalent-photon-approximation derivation that explains the γ-enhanced pressure and contrasting it with other calculations that may misbehave in massless limits. Overall, the work highlights how both mixing with heavy states and NLO soft emissions can substantially alter wall dynamics and, consequently, the gravitational-wave signatures from cosmological phase transitions.

Abstract

We analyse the dynamics of the relativistic bubble expansion during the first order phase transition focusing on the ultra relativistic velocities $γ\gg 1$. We show that fields much heavier than the scale of the phase transition can significantly contribute to the friction and modify the motion of the bubble wall leading to interesting phenomenological consequences. NLO effects on the friction due to the soft vector field emission are reviewed as well.

Bubble wall velocity: heavy physics effects

TL;DR

The paper analyzes the dynamics of relativistic bubble expansion during first-order phase transitions in the ultra-relativistic regime (γ ≫ 1). It demonstrates that heavy fields, even if decoupled at the transition scale, can impart significant friction on the bubble wall, potentially preventing runaway expansion, using a two-scalar toy model and a mixing mechanism. It reviews NLO friction arising from soft vector-boson emission, presenting an equivalent-photon-approximation derivation that explains the γ-enhanced pressure and contrasting it with other calculations that may misbehave in massless limits. Overall, the work highlights how both mixing with heavy states and NLO soft emissions can substantially alter wall dynamics and, consequently, the gravitational-wave signatures from cosmological phase transitions.

Abstract

We analyse the dynamics of the relativistic bubble expansion during the first order phase transition focusing on the ultra relativistic velocities . We show that fields much heavier than the scale of the phase transition can significantly contribute to the friction and modify the motion of the bubble wall leading to interesting phenomenological consequences. NLO effects on the friction due to the soft vector field emission are reviewed as well.

Paper Structure

This paper contains 14 sections, 85 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Transition pressure
  3. Leading order (LO) friction
  4. Friction from mixing
  5. Friction from mixing: more details
  6. Importance of friction from heavy particles
  7. NLO effects (review of Bodeker:2017cim)
  8. Equivalent photon approximation
  9. Another calculation of the NLO friction effects
  10. Summary
  11. Transition pressure
  12. Examples of the friction induced by the heavy particles
  13. Pressure from scalar mixing
  14. Pressure from scalar $1\to 2$ splitting

Figures (3)

  • Figure 1: Cartoon of a bubble wall interpolating between the values of the VEV of the scalar field in the symmetric and in the broken phase. The domain wall hitting the plasma in the symmetric phase induces a $A\to X$ transition.
  • Figure 2: Left- the potential difference and various contributions to the pressure as a function of the coupling $\lambda_{\phi\eta}$. The scale of the symmetry breaking was fixed to be $w=10^5$ GeV so that $\langle \phi \rangle\sim 10^5$ GeV. Right- The maximal mass of the heavy particle defined by the Eq.\ref{['eq:mmax']} as a function of $\lambda_{\phi\eta}$. As a typical width of the wall, we considered $L \sim 1/ \langle \phi\rangle$.
  • Figure 3: Illustration of the forward transmission pressure, the reflection pressure, the total pressure and the LO order approximation. $\frac{m_2}{T} = 10, 2$ respectively on the Left and the Right.