Hydrodynamic backreaction force of cosmological bubble expansion

Abstract

As a promising probe for the new physics beyond the standard model of particle physics in the early Universe, the predictions for the stochastic gravitational wave background from a cosmological firstorder phase transition heavily rely on the bubble wall velocity determined by the bubble expansion dynamics. The bubble expansion dynamics is governed by the competition between the driving force from the effective potential difference and the backreaction force from a sum of the thermal and friction forces induced by the temperature jumping and out-of-equilibrium effects across the bubble wall, respectively. Recently, a thermodynamic evaluation for the difference ∆[(γ 2 − 1)w] in the vicinity of the bubble wall is proposed to account for this backreaction force in a local thermal equilibrium from the enthalpy w and the Lorentz factor γ ≡ (1 − v2 ) −1/2 of the wall-frame fluid velocity v. However, this proposal has neglected the hydrodynamic contribution from the sound shell with a non-vanishing fluid velocity profile. In this paper, we propose a complete hydrodynamic evaluation on the backreaction force for a non-runaway bubble expansion, whose wall contribution exactly matches the previous thermodynamic evaluation.

Leptogenesis triggered by a first-order phase transition

“…[69] performs the first next-to-leading-order (NLO) calculation, showing that the emission of gauge bosons when particles cross the wall can induce a friction force scaling as P 1→2 ∝ γ w , preventing the bubble walls from runaway. Recently, friction force on the wall is studied in many literatures [70][71][72][73][74][75], and we take the results of refs. [70,71] to calculate the evolution of bubble walls.…”

Primordial black holes from slow phase transitions: a model-building perspective

“…Our work can be extended in several ways. While we have chosen v w = 1 as a benchmark value, it is important to consider the friction force induced by plasma particles, which typically leads to bubble wall velocities smaller than 1 [110][111][112][113][114][115]. By varying v w as different constants in our calculations, we find that lower values of v w result in later percolation and larger PBH abundance, with differences spanning several orders of magnitude.…”

The energy budget of cosmological first-order phase transitions beyond the bag equation of state

“…The nucleated bubbles then expand under the driving force given by the difference of the effective potential energy density between the false and true vacua. However, the bubble expansion is also subjected to the backreaction force [43] from the thermal plasma fluid, which consists of the thermal force from the temperature variation around the bubble wall and the friction force from the non-equilibrium effect in the vicinity of the bubble wall. When the total backreaction force could eventually balances the driving force, the bubble expansion is of non-runaway type with some temrminal wall velocity, otherwise, it is a runaway expansion approaching to the speed of light, which is considered to be unrealistic according to the recent debates [44][45][46][47][48][49][50][51][52][53][54][55].…”