Gravitational baryogenesis beyond the spectator approximation

Abstract

The standard gravitational-baryogenesis operator $\lambda {\nabla }_{\mu }R{J}^{\mu }$, with $\lambda \equiv \epsilon /M_{\ast }^2$, is usually treated as a spectator interaction that generates an effective chemical potential in a prescribed background. When included in the gravitational action, however, it defines a genuine curvature--matter-coupling variational problem, relevant for the baryon, lepton, and $B-L$ currents, whether described microscopically by particle-physics operators or macroscopically by a fluid current $J^{\mu }=n_X{u}^{\mu }$. Up to a boundary term the interaction is equivalent to $-\lambda R{\nabla }_{\mu }{J}^{\mu }$, making its $f(R,\mathrm{Matter})$ character manifest, but the metric equations remain open unless the metric dependence of $J^{\mu }$ is specified. For an arbitrary local realization $J^{\mu }(\Psi ,g)$ we derive the universal part of the field equations and isolate the realization-dependent tensor generated by ${\delta }_g{J}^{\mu }$. In the vector-density realization the explicit $J^{\alpha }{\nabla }_{\alpha }R$ term cancels, but an algebraic term $-\lambda g_{\mu \nu }R{\nabla }_{\alpha }{J}^{\alpha }$ survives, so the theory admits only a partial effective-Planck-mass interpretation, $M_{\mathrm{eff}}^2=M_{\mathrm{Pl}}^2-2\lambda {\nabla }_{\mu }{J}^{\mu }$, and a time-dependent effective gravitational coupling during baryogenesis. Specializing to flat Friedmann-Lemaître-Robertson-Walker (FLRW) with a homogeneous current $J^{\mu }=n_X{u}^{\mu }$, we obtain the modified Friedmann and Raychaudhuri equations, the associated continuity relation, and dimensionless diagnostics that quantify when the spectator approximation is controlled. We also discuss the implications for gravitational-baryogenesis studies in modified theories of gravity, providing a consistent General Relativity (GR) baseline for implementations in both standard cosmology and modified-gravity frameworks.

V2: 12 pages. Matches published version

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