Baryogenesis in $R^2$-Higgs inflation: The gravitational connection

$R^2$-Higgs inflation stands out as one of the best-fit models of Planck data. Using a covariant formalism for the inflationary dynamics and the production of helical gauge fields, we show that the observed baryon asymmetry of the Universe (BAU) can be obtained when this model is supplemented by a dimension-six $CP$-violating term $\sim (R/{\Lambda }^2)B_{\mu \nu }{\tilde{B}}^{\mu \nu }$ in the hypercharge sector. At linear order, values of $\Lambda \simeq 2.5\times {10}^{-5}{M}_P$ produce, in the $R^2$-like regime, sufficient helical hypermagnetic fields to create the observed matter-antimatter asymmetry during the electroweak crossover. However, the Schwinger effect of fermion pair production can play a critical role in this context, and that scale is significantly lowered when the backreaction of the fermion fields on the gauge field production is included. In all cases, the helical field configurations can remain robust against washout after the end of inflation.