Field-theoretic derivation of bubble-wall force

Abstract

We derive a general quantum field theoretic formula for the force acting on expanding bubbles of a first order phase transition in the early Universe setting. In the thermodynamic limit the force is proportional to the entropy increase across the bubble of active species that exert a force on the bubble interface. When local thermal equilibrium is attained, we find a strong friction force which grows as the Lorentz factor squared, such that the bubbles quickly reach stationary state and cannot run away. We also study an opposite case when scatterings are negligible across the wall (ballistic limit), finding that the force saturates for moderate Lorentz factors thus allowing for a runaway behavior. We apply our formalism to a massive real scalar field, the standard model and its simple portal extension. For completeness, we also present a derivation of the renormalized, one-loop, thermal energy-momentum tensor for the standard model and demonstrate its gauge independence.

On the perturbative expansion at high temperature and implications for cosmological phase transitions

“…For the bubble wall speed we simply take v w = 1 in the gravitational wave amplitude, noting that there remains considerable debate in the literature as to the leading effects which contribute to this quantity; see for example refs. [121,[124][125][126][127][128]. In the following, for simplicity, we will continue to use the same names for the approximations as in section 5, though one should bear in mind these additional limitations with regard to bubble nucleation and the bubble wall speed.…”

String fragmentation in supercooled confinement and implications for dark matter

“…This is the so-called ballistic regime, see e.g. [48], which will be useful for deriving the friction pressure in section 5.…”

Electroweak-like baryogenesis with new chiral matter

“…Here, κ sw is the efficiency factor of the sound wave and Hτ shock represents the reduction factor due to the short-lasting sound waves. We assume that the wall velocity is smaller than the sound velocity of the thermal plasma, v w c s ≡ 1/ √ 3 (i.e., the deflagration regime), which would be realized by the friction of the thermal plasma [127][128][129][130][131][132]. Under this assumption, κ sw can be fitted by the following formula as found in ref.…”