Non-equilibrium electroweak baryogenesis from preheating after inflation

TL;DR

The paper explores electroweak baryogenesis at the electroweak scale using a low-scale hybrid inflation model in which the Higgs field ends inflation. During preheating, non-thermal, long-wavelength bosonic modes become highly occupied, enhancing sphaleron transitions via an effective temperature $T_{eff}$ and enabling baryon-number generation through a dimension-six CP-violating operator that induces a chemical potential $\mu_{eff}$. The authors estimate $\Gamma_{sph} \sim \alpha_W^4 T_{eff}^4$ and derive $n_B/s$ expressions that, with plausible parameters ($M_{new}\sim 1~\text{TeV}$, $\delta_{CP}\sim 10^{-3}$), match the observed baryon asymmetry, with reheating temperatures $T_{rh} < 100$ GeV preventing washout. Numerical simulations in (1+1) dimensions support the mechanism, showing rapid population of infrared modes, diffusion of Chern-Simons number, and a baryon asymmetry that freezes in after preheating as the system thermalizes. Overall, the work presents a viable non-equilibrium route to electroweak baryogenesis at TeV scales, relying on preheating dynamics and CP-violating new physics accessible at TeV energies.

Abstract

We present a novel scenario for baryogenesis in a hybrid inflation model at the electroweak scale, in which the Standard Model Higgs field triggers the end of inflation. One of the conditions for successful baryogenesis, the departure from thermal equilibrium, is naturally achieved at the stage of preheating after inflation. The inflaton oscillations induce large occupation numbers for long-wavelength configurations of Higgs and gauge fields, which leads to a large rate of sphaleron transitions. We estimate this rate during the first stages of reheating and evaluate the amount of baryons produced due to a particular type of higher dimensional CP violating operator. The universe thermalizes through fermion interactions, at a temperature below critical, $T_{rh} < 100$ GeV, preventing the wash-out of the produced baryon asymmetry. Numerical simulations in (1+1) dimensions support our theoretical analysis.

Figures (15)

• Figure 1: The projected effective potential $V(\sigma)/V_0$, for the inflaton field $\sigma/\sigma_c$ after the end of inflation. The dashed line corresponds to the $m^2\sigma^2$ approximation around the minimum of the inflaton potential. Due to the shape of the potential at large $\sigma$, initial large-amplitude oscillations of the field $\sigma$ are not exactly harmonic.
• Figure 2: The growth parameter $\mu_k$ as a function of momenta $k$, in units of $m$, for a Higgs mass $m_{_{\rm H}} = 350$ GeV. The occupation numbers for each mode $k$ can be obtained from $n_k=\exp(2\mu_k mt)/2$.
• Figure 3: The evolution of the Higgs spectrum $n_k\,\omega_k$, in units of $v=246$ GeV, from time 0 to $10^4$$v^{-1}$, as a function of momentum, $k/m$. The initial spectrum is set by preheating, and contains a set of narrow bands (solid line). The subsequent evolution of the system leads to a redistribution of energy between different modes. Note how rapidly a "thermal" equidistribution is reached for the long-wavelength modes. However, the whole Higgs spectrum approaches thermalization already in the middle of resonance (see Fig. \ref{['fig7']} below).
• Figure 4: The time evolution of the inflaton energy, the Higgs energy and the total energy. Note that the energy is measured in units of $v$ and time in units of $v^{-1}$, see Ref. grsnpb.
• Figure 5: The time evolution of the effective temperature, in units of $v$. We have averaged the Higgs power spectrum over different low-momentum regions, and we obtain several effective temperatures that show different time behavior.