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

Abstract

We propose \emph{Scalar-Tensor Baryogenesis} (STB), in which the $CP$-violating bias needed for baryogenesis is sourced by the \emph{gravitational} scalars that appear in scalar-tensor representations of modified gravity. Derivative couplings $M_{\ast }^{-d}{\nabla }_{\mu }f({\varphi }_i)J_{B-L}^{\mu }$ 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 $F(R)=R^{1+\epsilon }$ with $B-L$ violation from the dimension-five Weinberg operator, and reproduce the observed baryon asymmetry for $\epsilon =\mathcal{O}(10^{-6})$ with $T_D\simeq 8.5\times 10^{13}\mathrm{GeV}$ and negligible backreaction, while satisfying nucleosynthesis bounds and keeping the expansion arbitrarily close to the GR radiation solution.

arXiv comment12 pages, 1 figure

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