A Numerical Relation Between the Baryon Asymmetry, the CMB Temperature, and the Electron Mass

Abstract

We report a numerical relation connecting the baryon-to-photon ratio $\eta$, the CMB temperature $T_{\rm CMB}$, and the electron mass $m_e$:

The relation predicts $\eta = 6.128 \times 10^{-10}$, within 0.03% of the Planck 2018 value — well inside the current 1σ measurement uncertainty. The coefficient $4/3$ is the radiation enthalpy factor ($\rho + P = \tfrac{4}{3}\rho$ for a relativistic gas), and the relation admits a direct physical reading: the electron rest energy equals the radiation enthalpy per baryon in the present universe. Among all sixteen Standard Model particles, the electron is the only one that yields a simple rational coefficient. The relation is consistent with all independent determinations of $\eta$ from CMB experiments (Planck, ACT, SPT, WMAP) and Big Bang nucleosynthesis, is not a consequence of any known equation in standard cosmology, and does not appear in the published literature. We discuss the physical interpretation as a matter–radiation enthalpy balance analogous to the virial theorem, the connection to the electron Yukawa coupling ($Y_B \approx 10\,y_e^2$), and nine attempted derivation paths.

DOI

https://doi.org/10.5281/zenodo.19643297