Michael Ramsey-Musolf

Early Universe Bubble Nucleation

If a first order phase transition occurred in the early universe, it would proceed through bubble nucleation. As the figure illustrates, during a first order electroweak phase transition, electroweak symmetry-breaking (EWSB) occurs in the bubble interiors in a symmetric phase background. The bubbles expand, collide, and merge, eventually filling the observable universe with regions of broken symmetry. The bubble nucleation rate is a critical factor in determining whether the matter-antimatter asymmetry could have been generated during an electroweak phase transition and whether the echoes of bubble collisions could be observed in next generation gravitational wave searches.

Computing the bubble nucleation rate in a reliable manner is an important theoretical challenge. My collaborators and I recently solved a long-standing theoretical problem at this forefront: how to compute the nucleation rate perturbatively in a gauge-invariant manner when the quantum corrections generate the potential barrier between the symmetry and broken phases. Read the details in our two resulting papers:

• Lofgren, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and P. Schicho, Phys. Rev. Lett. 130 (2023) 251801
• Hirvonen, J. Lofgren, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and P. Schicho, JHEP 07 (2022) 135

As illustrated in the figure below, the basic idea is to re-organize the perturbative expansion by adopting an appropriate power-counting in the couplings of the theory. One may then expand the 3D effective action to next-to-leading order (NLO) in the coupling. The coefficients of the first two terms in this expansion are gauge-invariant, providing a self-consistent NLO computation of the thermodynamic factor in the nucleation rate. One must rely on non-perturbative methods to obtain higher-order contributions ∆.