David S. Pereira
We propose Scalar–Tensor Baryogenesis (STB), in which the CP -violating bias needed for baryogenesis is sourced by the gravitational scalars that appear in scalar–tensor representations of modified gravity. Derivative couplings M * − d ∇ μ f ( ϕ i ) J B − L μ act as an effective chemical potential μ B − L ∝ f ˙ in an FRW background, driving the plasma to a nonzero equilibrium B − L density while B − L -violating reactions are active. The asymmetry freezes in at the dynamically determined decoupling temperature T D fixed by Γ B − L ( T D ) = H ( T D ) , giving n b / s ∝ [ f ˙ / ( M * d T ) ] T D up to sphaleron conversion. A key structural result is an explicit on-shell/background map—through the Legendre relations defining the scalar potential—between curvature-based geometric Gravitational baryogenesis operators and their scalar–tensor counterparts, together with a canonical Einstein-frame description closely paralleling spontaneous/quintessential baryogenesis, but with a gravitational (not ad hoc matter) biasing field. The map is not a mere change of variables: it imposes consistency conditions (existence of the scalar–tensor branch, local invertibility of the Legendre map, and validity of the spectator regime), thereby restricting the admissible operator space and tying μ B − L ∝ f ˙ to the modified-gravity dynamics once F is specified. As an illustration, we implement STB in F ( R ) = R 1 + ε with B − L violation from the dimension-five Weinberg operator, and reproduce the observed baryon asymmetry for ε = O ( 10 − 6 ) with T D ≃ 8.5 × 10 13 GeV and negligible backreaction, while satisfying nucleosynthesis bounds and keeping the expansion arbitrarily close to the GR radiation solution.