Chern-Simons production during preheating in hybrid inflation models

TL;DR

The study investigates Chern-Simons number production during tachyonic preheating after hybrid inflation in a (3+1)D SU(2) gauge–scalar sector coupled to a singlet inflaton, using a classical lattice approximation for the infrared dynamics. It demonstrates that CS generation is driven by local sphaleron-like structures and remains robust to ultraviolet and infrared cutoffs, with a measurable sphaleron rate on the order of $\Gamma \sim 10^{-5} m^4$ in favorable parameter regimes. The results establish a link between Chern-Simons production and localized topological structures, and they show that, in the presence of a CP-violating operator, this mechanism can yield a viable baryon asymmetry at electroweak scales during preheating. The work provides a quantitative framework for baryogenesis in out-of-equilibrium post-inflation dynamics and highlights the need for including CP violation and potentially the full ${\rm SU(2)}\times{\rm U(1)}$ sector in future simulations. $$\text{I(mt)}= m\int_{t_i}^{t} dt'\, \Gamma(t')$$ and $$n_B/s \sim \Gamma_{\rm sph}\,\mu_{\rm eff}/T_{\rm eff}$$ under reasonable assumptions illustrate the magnitude of the effect.

Abstract

We study the onset of symmetry breaking after hybrid inflation in a model having the field content of the SU(2) gauge-scalar sector of the standard model, coupled to a singlet inflaton. This process is studied in (3+1)-dimensions in a fully non-perturbative way with the help of lattice techniques within the classical approximation. We focus on the role played by gauge fields and, in particular, on the generation of Chern-Simons number. Our results are shown to be insensitive to the various cut-offs introduced in our numerical approach. The spectra preserves a large hierarchy between long and short-wavelength modes during the whole period of symmetry breaking and Chern-Simons generation, confirming that the dynamics is driven by the low momentum sector of the theory. We establish that the Chern-Simons production mechanism is associated with local sphaleron-like structures. The corresponding sphaleron rates are of order 10^{-5} m^4, which, within certain scenarios of electroweak baryogenesis and a (not unnaturally large) additional source of CP violation, could explain the present baryon asymmetry of the universe.

Figures (15)

• Figure 1: Left: The time evolution of the spatial averages of the normalized Higgs field ($\overline{ |\phi|}/v$) and inflaton ($\overline{\chi}/\chi_c$) for a single configuration of model A ($\lambda=g^2/2=0.00675$, $V=0.024$) and various values of the gauge coupling $g_{_{\rm W}}$ (see Table \ref{['models']}). Right: The time evolution of the top of the highest lump $|\phi|_{\rm peak}/v$.
• Figure 2: The time evolution of the energy fractions for a single configuration of model A and various values of the gauge coupling $g_{_{\rm W}}$.
• Figure 3: Left: The UV cutoff dependence of the normalized $\langle \overline{|\phi|}\rangle$ and $\langle \overline{\chi} \rangle$ and average electric and magnetic energy fractions. Right: The volume dependence of $\langle \overline{|\phi|}\rangle$ and $\langle \overline{\chi}\rangle$ and average electric and magnetic energy fractions. Parameters as in model A1 in Table \ref{['models']}.
• Figure 4: The time evolution of $\langle \overline{|\phi|}/v\rangle$, $\langle \overline{\chi}/\chi_c\rangle$ and gauge energy fractions for two different initial times $mt_i=5$ and $mt_i=6.5$ (model A1).
• Figure 5: Dependence on the UV cutoff of the Fourier spectra of the (pure gauge) electric energy and Higgs-inflaton contribution to the potential energy evaluated at $mt=5$, 12 and 20. Results are averaged over 10 configurations with $\lambda=g^2/2=0.00675$, $V=0.024$, and $g_{_{\rm W}}=0.05$ (model A1), and $mt_i=5$.