Scalar-tensor baryogenesis: a scalar-tensor completion of gravitational baryogenesis

We propose \emph{Scalar-Tensor Baryogenesis} (STB), in which the $C\!P$-violating bias needed for baryogenesis is sourced by the \emph{gravitational} scalars that appear in scalar-tensor representations of modified gravity. Derivative couplings $M_\ast^{-d}\nabla_\mu f(\phi_i)\,J^\mu_{B-L}$ act as an effective chemical potential $\mu_{B-L}\propto\dot f$ 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 $\Gamma_{B-L}(T_D)=H(T_D)$, giving $n_b/s\propto[\dot f/(M_\ast^d T)]_{T_D}$ up to sphaleron conversion. A key structural result is an explicit \emph{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 $\mu_{B-L}\propto\dot f$ to the modified-gravity dynamics once $F$ is specified. As an illustration, we implement STB in $F(R)=R^{1+\varepsilon}$ with $B\!-\!L$ violation from the dimension-five Weinberg operator, and reproduce the observed baryon asymmetry for $\varepsilon=\mathcal{O}(10^{-6})$ with $T_D\simeq 8.5\times10^{13}\,\mathrm{GeV}$ and negligible backreaction, while satisfying nucleosynthesis bounds and keeping the expansion arbitrarily close to the GR radiation solution.