Resonant amplification of electroweak baryogenesis at preheating

We explore viable scenarios for parametric resonant amplification of electroweak (EW) gauge fields and the Chern-Simons number during preheating, leading to baryogenesis at the EW scale. In this class of scenarios time-dependent classical EW gauge fields, essentially spatially homogeneous on the horizon scales, carry the Chern-Simons number which can be amplified by parametric resonance up to magnitudes at which unsuppressed topological transitions in the Higgs sector become possible. Baryon number nonconservation associated with the gauge sector and the highly non-equilibrium nature of preheating allow for efficient baryogenesis. The requisite large $\mathrm{CP}$ violation can arise either from the time dependence of a slowly varying Higgs field (spontaneous baryogenesis) or from a resonant amplification of $\mathrm{CP}$ violation induced in the gauge sector through loops. We identify several $\mathrm{CP}$-violating operators in the standard model and its minimal extensions that can facilitate efficient baryogenesis at preheating, and we show how to overcome would-be exponential suppression of baryogenesis associated with tunneling barriers.