Logarithmically divergent friction on ultrarelativistic bubble walls

TL;DR

This paper calculates the friction on ultrarelativistic bubble walls during a specific particle transition, revealing a logarithmic dependence on the Lorentz factor, which refines previous estimates and impacts cosmological phase transition models.

Contribution

It provides a detailed numerical analysis of friction with finite-wall-width effects, showing a logarithmic dependence on wall velocity, and compares this to other friction sources in phase transitions.

Findings

Friction scales logarithmically with the Lorentz factor γ_w.

Friction from the light-to-heavy transition is smaller than from dark matter particle transmission.

Numerical fit accurately captures the frictional pressure dependence.

Abstract

We calculate the friction experienced by ultrarelativistic bubble walls resulting from the $1 \rightarrow 2$ light-to-heavy transition process, with finite-wall-width effects fully taken into account. In this process, the light particle is excited from the order-parameter scalar field, while the two heavy particles are excitations of a dark matter scalar field. Unlike earlier estimates suggesting a friction scaling as $\gamma_w^0$, where $\gamma_w$ represents the Lorentz factor of the wall velocity, our more precise numerical analysis reveals a logarithmic dependence of the friction on $\gamma_w$. We offer a numerical fit to capture this frictional pressure accurately. Our analysis verifies that the friction stemming from the $1 \rightarrow 2$ light-to-heavy transition is typically much smaller than the friction from the $1 \rightarrow 1$ transmission of the dark matter particles.