Effective picture of bubble expansion

Abstract

Recently the thermal friction on an expanding bubble from the cosmic first-order phase transition has been calculated to all orders of the interactions between the bubble wall and thermal plasma, leading to a ${\gamma }^2$-scaling instead of the previously estimated ${\gamma }^1$-scaling for the thermal friction exerted on a fast-moving bubble wall with a Lorentz factor $\gamma$. We propose for the first time the effective equation of motion (EOM) for an expanding bubble wall in the presence of an arbitrary $\gamma$-scaling friction to compute the efficiency factor from bubble collisions, which, in the case of ${\gamma }^2$-scaling friction, is found to be larger than the recently updated estimation when the bubble walls collide after starting to approach a constant terminal velocity, leading to a slightly larger signal of the gravitational waves background from bubble collisions due to its quadratic dependence on the bubble collision efficiency factor, although the ${\gamma }^2$-scaling friction itself has already suppressed the contribution from bubble collisions compared to that with ${\gamma }^1$-scaling friction. We also suggest a phenomenological parameterization for the out-of-equilibrium term in the Boltzmann equation that could reproduce the recently found $({\gamma }^2-1)$-scaling of the friction term in the effective EOM of an expanding bubble wall, which merits further study in future numerical simulations of bubble expansion and collisions.

v1, 26 pages, 2 figures; v2, typos corrected and references added; v3, minor improvements in presentation

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Cited by in corpus (5)

• The Gravitational-Wave Physics II: Progress
• Bubble wall dynamics at the electroweak phase transition
• A sonic boom in bubble wall friction
• Gravitational Waves from the Cosmological Quark-Hadron Phase Transition Revisited
• Dynamics of bubble walls at the electroweak phase transition