Nonperturbative Analysis of the Electroweak Phase Transition in the Two Higgs Doublet Model

Nucleation at Finite Temperature: A Gauge-Invariant Perturbative Framework

We present a gauge-invariant framework for bubble nucleation in theories with radiative symmetry breaking at high temperature. As a procedure, this perturbative framework establishes a practical, gauge-invariant computation of the leading order nucleation rate, based on a consistent power counting in the high-temperature expansion. In model building and particle phenomenology, this framework has applications such as the computation of the bubble nucleation temperature and the rate for electroweak baryogenesis and gravitational wave signals from cosmic phase transitions.

Domain Walls Seeding the Electroweak Phase Transition

Topological defects can act as local impurities that seed cosmological phase transitions. In this Letter, we study the case of domain walls and how they can affect the electroweak phase transition in the singlet-extended standard model with a Z_{2}-symmetric potential. When the transition occurs in two steps, the early breaking of the Z_{2} symmetry implies the formation of domain walls which then act as nucleation sites for the second step. We develop a method based on a Kaluza-Klein decomposition to calculate the rate of the catalyzed phase transition within the 3D theory on the domain wall surface. By comparison with the standard homogeneous rate, we conclude that the seeded phase transition is generically faster and it ultimately determines the way the phase transition is completed. We finally comment on the phenomenological implications for gravitational waves.

Constraining Cosmological Phase Transitions with the Parkes Pulsar Timing Array

A cosmological first-order phase transition is expected to produce a stochastic gravitational wave background. If the phase transition temperature is on the MeV scale, the power spectrum of the induced stochastic gravitational waves peaks around nanohertz frequencies, and can thus be probed with high-precision pulsar timing observations. We search for such a stochastic gravitational wave background with the latest data set of the Parkes Pulsar Timing Array. We find no evidence for a Hellings-Downs spatial correlation as expected for a stochastic gravitational wave background. Therefore, we present constraints on first-order phase transition model parameters. Our analysis shows that pulsar timing is particularly sensitive to the low-temperature (T∼1-100  MeV) phase transition with a duration (β/H_{*})^{-1}∼10^{-2}-10^{-1} and therefore can be used to constrain the dark and QCD phase transitions.

Magnetic Field and Gravitational Waves from the First-Order Phase Transition

We perform the three-dimensional lattice simulation of the magnetic field and gravitational wave productions from bubble collisions during the first-order electroweak phase transition. Except for the gravitational wave, the power-law spectrum of the magnetic field strength is numerically calculated for the first time, which is of a broken power-law spectrum: B_{ξ}∝f^{0.91} for the low-frequency region of f<f_{⋆} and B_{ξ}∝f^{-1.65} for the high-frequency region of f>f_{⋆} in the thin-wall limit, with the peak frequency being f_{⋆}∼5  Hz at the phase transition temperature 100 GeV. When the hydrodynamics is taken into account, the generated magnetic field strength can reach B_{ξ}∼10^{-7}  G at a correlation length ξ∼10^{-7}  pc, which may seed the large scale magnetic fields. Our study shows that the measurements of cosmic magnetic field strength and gravitational waves are complementary to probe new physics admitting electroweak phase transition.