TY - JOUR

T1 - Bubble wall velocities in local equilibrium

AU - Ai, Wen Yuan

AU - Garbrecht, Björn

AU - Tamarit, Carlos

N1 - Publisher Copyright:
© 2022 IOP Publishing Ltd and Sissa Medialab.

PY - 2022/3

Y1 - 2022/3

N2 - It is commonly expected that a friction force on the bubble wall in a first-order phase transition can only arise from a departure from thermal equilibrium in the plasma. Recently however, it was argued that an effective friction, scaling as 32 w (with 3 w being the Lorentz factor for the bubble wall velocity), persists in local equilibrium. This was derived assuming constant plasma temperature and velocity throughout the wall. On the other hand, it is known that, at the leading order in derivatives, the plasma in local equilibrium only contributes a correction to the zero-temperature potential in the equation of motion of the background scalar field. For a constant plasma temperature, the equation of motion is then completely analogous to the vacuum case, the only change being a modified potential, and thus no friction should appear. We resolve these apparent contradictions in the calculations and their interpretation and show that the recently proposed effective friction in local equilibrium originates from inhomogeneous temperature distributions, such that the 32 w -scaling of the effective force is violated. Further, we propose a new matching condition for the hydrodynamic quantities in the plasma valid in local equilibrium and tied to local entropy conservation. With this added constraint, bubble velocities in local equilibrium can be determined once the parameters in the equation of state are fixed, where we use the bag equation in order to illustrate this point. We find that there is a critical value of the transition strength αcrit such that bubble walls run away for α>αcrit.

AB - It is commonly expected that a friction force on the bubble wall in a first-order phase transition can only arise from a departure from thermal equilibrium in the plasma. Recently however, it was argued that an effective friction, scaling as 32 w (with 3 w being the Lorentz factor for the bubble wall velocity), persists in local equilibrium. This was derived assuming constant plasma temperature and velocity throughout the wall. On the other hand, it is known that, at the leading order in derivatives, the plasma in local equilibrium only contributes a correction to the zero-temperature potential in the equation of motion of the background scalar field. For a constant plasma temperature, the equation of motion is then completely analogous to the vacuum case, the only change being a modified potential, and thus no friction should appear. We resolve these apparent contradictions in the calculations and their interpretation and show that the recently proposed effective friction in local equilibrium originates from inhomogeneous temperature distributions, such that the 32 w -scaling of the effective force is violated. Further, we propose a new matching condition for the hydrodynamic quantities in the plasma valid in local equilibrium and tied to local entropy conservation. With this added constraint, bubble velocities in local equilibrium can be determined once the parameters in the equation of state are fixed, where we use the bag equation in order to illustrate this point. We find that there is a critical value of the transition strength αcrit such that bubble walls run away for α>αcrit.

KW - cosmological phase transitions

KW - physics of the early universe

UR - http://www.scopus.com/inward/record.url?scp=85126442539&partnerID=8YFLogxK

U2 - 10.1088/1475-7516/2022/03/015

DO - 10.1088/1475-7516/2022/03/015

M3 - Article

AN - SCOPUS:85126442539

SN - 1475-7516

VL - 2022

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

IS - 3

M1 - 015

ER -