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

David S. Pereira

Abstract

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 $M_\ast^{-d}\nabla_μf(φ_i)\,J^μ_{B-L}$ act as an effective chemical potential $μ_{B-L}\propto\dot f$ 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 $Γ_{B-L}(T_D)=H(T_D)$, 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 $μ_{B-L}\propto\dot f$ 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.

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

Abstract

We propose \emph{Scalar-Tensor Baryogenesis} (STB), in which the -violating bias needed for baryogenesis is sourced by the \emph{gravitational} scalars that appear in scalar-tensor representations of modified gravity. Derivative couplings act as an effective chemical potential in an FRW background, driving the plasma to a nonzero equilibrium density while -violating reactions are active. The asymmetry freezes in at the dynamically determined decoupling temperature fixed by , giving 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 to the modified-gravity dynamics once is specified. As an illustration, we implement STB in with violation from the dimension-five Weinberg operator, and reproduce the observed baryon asymmetry for with and negligible backreaction, while satisfying nucleosynthesis bounds and keeping the expansion arbitrarily close to the GR radiation solution.

Paper Structure

This paper contains 12 sections, 2 theorems, 85 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Scalar-tensor gravity
  3. General scalar-tensor representation
  4. Scalar-tensor Baryogenesis
  5. Baryon asymmetry generation
  6. Einstein frame formalism
  7. Relation between gravitational baryogenesis and scalar-tensor baryogenesis
  8. GB $\to$ STB map
  9. STB $\to$ GB map
  10. Application of STB
  11. Field Equations and Cosmological Dynamics for Baryogenesis
  12. Summary and discussion

Key Result

Proposition 1

Let a modified-gravity theory with action geometrical admit a scalar--tensor representation stt geral such that $x_i=\chi_i$ follows from the auxiliary-field equations (equivalently, $\det M\neq 0$ in the region of interest), and assume that the Legendre map is locally invertible so that $V(\phi_1,\ admits the on-shell/background rewriting i.e. it can be expressed in scalar--tensor language with

Figures (1)

  • Figure 1: Baryon asymmetry yield $n_b/s$ as a function of $\varepsilon$ for the model $F(R)=R^{1+\varepsilon}$, evaluated with $M_\ast=M_{\rm Pl}$, $\mathrm{c}_{\text{STB}}=-3$, and the minimal normal-ordering benchmark $\bar{m}_\nu^{\,2}\simeq 2.6\times10^{-3}\,\mathrm{eV}^2$. The shaded region denotes the observational interval $(8.8\pm0.6)\times10^{-11}$. The markers indicate representative intersections with the lower, central, and upper values of the band: $\varepsilon_\circ = 3.484770\times10^{-6}$ ($8.2\times10^{-11}$), $\varepsilon_\Box = 3.739751\times10^{-6}$ ($8.8\times10^{-11}$), and $\varepsilon_\triangle = ~ 3.994731\times10^{-6}$ ($9.4\times10^{-11}$).

Theorems & Definitions (2)

  • Proposition 1: On-shell/background dictionary for GB$\rightarrow$STB operators
  • Proposition 2: STB$\rightarrow$GB pull-back