Electroweak preheating on a lattice

TL;DR

The paper investigates whether baryogenesis can arise from non-thermal electroweak symmetry restoration during preheating at the electroweak scale. Using classical lattice simulations of a bosonic $SU(2)\times U(1)$ + Higgs system with damping to mimic fermions, it tracks the evolution of the Chern-Simons number and the effective temperature of long-wavelength modes after energy transfer from the inflaton to the Higgs sector. The results reveal non-thermal restoration with non-Brownian, predominantly non-topological fluctuations in $N_{CS}$ and no net baryon-number generation in CP-invariant runs, suggesting that CP violation and inflaton coupling must be included for quantitative baryogenesis predictions. The study provides a principled framework to explore preheating-induced baryogenesis and highlights the role of gauge-Higgs interactions in suppressing topological transitions, guiding future CP-violating extensions.

Abstract

In many inflationary models, a large amount of energy is transferred rapidly to the long-wavelength matter fields during a period of preheating after inflation. We study how this changes the dynamics of the electroweak phase transition if inflation ends at the electroweak scale. We simulate a classical SU(2)xU(1)+Higgs model with initial conditions in which the energy is concentrated in the long-wavelength Higgs modes. With a suitable initial energy density, the electroweak symmetry is restored non-thermally but broken again when the fields thermalize. During this symmetry restoration, baryon number is violated, and we measure its time evolution, pointing out that it is highly non-Brownian. This makes it difficult to estimate the generated baryon asymmetry.

Figures (6)

• Figure 1: Evolution near the vacuum for a renormalized (bottom) and non renormalized (top) mass term with $g=g'=0.1$ and $a=$$2,3,4\times 10^{-3}$ GeV$^{-1}$. The straight line is $\eta^2$.
• Figure 2: Measuring $N_{\rm CS}$ with different cooling paths. The path lengths are 0. 0.9$a^2$,1.8$a^2$, 4.5$a^2$, 9.0$a^2$. Without cooling, the ultraviolet noise blurs the signal, but with cooling the sphaleron can be seen at $t=0.1~{\rm GeV}^{-1}$.
• Figure 3: The evolution of the renormalised $|\phi|^2$ defined in Eq. (\ref{['equ:phisqcounter']}) as a function of time. Because of the inhomogeneous fluctuations, $|\phi|^2$ never vanishes, but its exponential decay shows that the electroweak symmetry is effectively restored up until $t\mathop{\hbox{$>$$\sim$}} 0.8$ GeV$^{-1}$
• Figure 4: Effective temperature (\ref{['equ:Teff']}) of different Fourier modes of the hypercharge field measured in the initial configuration and at $t=0.1~{\rm GeV}^{-1}$. At this time, the Higgs fluctuations have heated up the long-wavelength modes to a high effective temperature. For comparison, the plot also shows the effect of the damping term to the vacuum, measured in a run with $\phi_0=0$.
• Figure 5: $\langle N_{\rm CS}^2\rangle$ for dissipation $\gamma=2$ GeV$^{-1}$ (top) and $\gamma=0$ (bottom) with a cooling depth of $0.9a^2$, averaged over 12 runs. Initially $\langle N_{\rm CS}^2\rangle$ oscillates and then starts to decrease vanishing eventually, which means that no topological transitions actually took place. In thermal equilibrium, $\langle N_{\rm CS}^2\rangle$ would grow linearly, which is what happens in the dissipationless run at late times.