Thermal pressure on ultrarelativistic bubbles from a semiclassical formalism

TL;DR

This paper investigates the thermal pressure on ultrarelativistic bubble walls during early universe phase transitions using a semiclassical formalism, analyzing radiation spectra and momentum transfer for different wall models.

Contribution

It introduces a semiclassical current radiation formalism to compute radiation spectra and thermal pressure on ultrarelativistic bubble walls, considering wall thickness effects and emission regimes.

Findings

SCR formalism reproduces known pressure scaling in soft emission regime

Wall thickness L_w cuts off high-momentum radiation spectrum

Emission spectrum depends on whether deceleration is abrupt or gradual

Abstract

We study a planar bubble wall that is traveling at an ultrarelativistic speed through a thermal plasma. This situation may arise during a first-order electroweak phase transition in the early universe. As particles cross the wall, it is assumed that their mass grows from $m_a$ to $m_b$, and they are decelerated causing them to emit massless radiation ($m_c=0$). We are interested in the momentum transfer to the wall, the thermal pressure felt by the wall, and the resultant terminal velocity of the wall. We employ the semiclassical current radiation (SCR) formalism to perform these calculations. An incident-charged particle is treated as a point-like classical electromagnetic current, and the spectrum of quantum electromagnetic radiation (photons) is derived by calculating appropriate matrix elements. To understand how the spectrum depends on the thickness of the wall, we explore simplified models for the current corresponding to an abrupt and a gradual deceleration. For the model of abrupt deceleration, we find that the SCR formalism can reproduce the $P_\mathrm{therm} \propto \gamma_w^0$ scaling found in earlier work by assuming that the emission is soft, but if the emission is not soft the SCR formalism can be used to obtain $P_\mathrm{therm} \propto \gamma_w^2$ instead. For the model of gradual deceleration, we find that the wall thickness $L_w$ enters to cutoff the otherwise log-flat radiation spectrum above a momentum of $\sim \gamma_w^2 / L_w$, and we discuss the connections with classical electromagnetic bremsstrahlung.