  If the inflaton field is coupled to the hypercharge Chern-Simons density
$F\tilde F$, an explosive production of helical gauge fields when inflation
ends can trigger baryogenesis at the electroweak phase transition. Besides,
Higgs inflation identifies the inflaton with the Higgs field $\mathcal H$, thus
relating cosmological observables to properties of electroweak physics. In this
paper we merge both approaches: the helical gauge fields are produced at the
end of Higgs inflation from the coupling $|\mathcal H|^2 F\tilde F$. In the
metric formulation of gravity we found a window in the parameter space for
electroweak baryogenesis consistent with all experimental observations.
Conversely, for the Palatini formalism the non-gaussianity bounds strongly
constrain the helicity produced at the end of inflation, forbidding an
efficient baryogenesis.
