Early-universe constraints on the electron mass

We investigate the impact of a nonstandard electron mass $m_e$ on early-Universe thermal history, focusing on neutrino decoupling and Big Bang Nucleosynthesis (BBN). In the standard cosmology, neutrino–electron interactions keep neutrinos in thermal contact with the electromagnetic plasma until shortly before $e^\pm$ annihilation. Varying $m_e$ shifts the decoupling epoch and the entropy transfer from $e^\pm$ annihilation, thereby modifying the neutrino energy density and the inferred effective number of relativistic species, $N_{\mathrm{eff}}$. Independently, during BBN the rates of charged-current weak processes, and hence the neutron-to-proton ratio, depend on $m_e$. By confronting BBN predictions for the primordial light-element abundances with observations and imposing cosmological constraints on $N_{\mathrm{eff}}$, we obtain a bound on $m_e$ in the early Universe of $m_e = 0.504^{+0.007}_{-0.006}$ MeV or $m_e=0.510\pm0.007$ MeV ($1σ$), depending on the considered nuclear reaction network (NACRE II or PRIMAT, respectively). The allowed range is close to the present laboratory value at the level of 1.4%, thus supporting the constancy of the electron mass over cosmological timescales.

💡 Research Summary

**
The paper investigates how a deviation of the electron mass, $m_e$, from its laboratory value would affect two key epochs of the early Universe: neutrino decoupling (around a few MeV) and Big‑Bang Nucleosynthesis (BBN, at temperatures of order 0.1–0.01 MeV). In the standard ΛCDM picture, weak interactions keep neutrinos in thermal contact with the electromagnetic plasma until just before electron–positron annihilation. When $e^\pm$ pairs annihilate, their entropy is transferred primarily to photons, raising the photon temperature relative to the neutrinos and fixing the effective number of relativistic species, $N_{\rm eff}\simeq3.044$.

If $m_e$ were larger, the $e^\pm$ mass threshold would be reached earlier, so annihilation would occur while neutrinos are still tightly coupled. A larger fraction of the released entropy would then be shared with the neutrino sector, reducing the photon heating and increasing $N_{\rm eff}$ (up to the limiting value $N_{\rm eff}\rightarrow 11.56$ when neutrinos stay fully coupled). Conversely, a smaller $m_e$ delays annihilation, allowing neutrinos to decouple earlier; the entropy then goes almost entirely into photons, and $N_{\rm eff}$ approaches the standard value.

To quantify these effects, the authors modify the public NUDEC_BSM code, introducing a free parameter $k=m_e/m_0$ while keeping the comoving variable $x’=m_0 a$ fixed. They solve the coupled continuity equation for the total energy‑momentum tensor and the Liouville (Boltzmann) equation for each neutrino flavor, assuming Fermi‑Dirac spectra with a common temperature for each flavor, vanishing chemical potentials, and neglecting neutrino oscillations. Finite‑temperature QED corrections to the electron‑photon plasma are included. The resulting evolution of the comoving photon temperature $z_\gamma$ and the neutrino temperatures $z_{\nu_e}$ and $z_{\nu_{\mu,\tau}}$ is displayed for three illustrative masses (0.1 MeV, 0.511 MeV, 5 MeV). The corresponding $N_{\rm eff}$ as a function of $m_e$ reproduces the standard value at $m_e=0.511$ MeV and shows the expected monotonic increase for larger masses.

The second part of the analysis focuses on BBN. The neutron‑to‑proton ratio, set by weak interaction rates that depend on $m_e$ (through phase‑space factors and the $Q$‑value of the $n\leftrightarrow p$ conversion), freezes out at $T_{\rm fr}\sim1$ MeV. After freeze‑out, neutrons decay until nuclear reactions begin at $T\sim0.07$ MeV, forming deuterium, helium‑3, tritium, and finally helium‑4. The authors compute the primordial abundances using two modern nuclear reaction networks: NACRE II and PRIMAT. They adopt observational constraints on deuterium (D/H = $(2.547\pm0.029)\times10^{-5}$) and helium‑4 mass fraction ($Y_p=0.245\pm0.003$), together with CMB‑derived values for the baryon‑to‑photon ratio ($\eta_{10}=6.040\pm0.118$) and $N_{\rm eff}=3.04\pm0.33$.

A Bayesian likelihood analysis combines the BBN predictions (which depend on $m_e$ through both weak rates and the altered $N_{\rm eff}$) with the observational data. The resulting posterior distributions give $m_e=0.504^{+0.007}_{-0.006}$ MeV when the NACRE II network is used, and $m_e=0.510\pm0.007$ MeV for the PRIMAT network, both at the 1σ level. These values are within 1.4 % of the laboratory electron mass $m_e^{\rm lab}=0.511$ MeV, indicating no statistically significant deviation.

The authors conclude that the electron mass has remained constant to within a few parts per hundred from the MeV epoch of the early Universe to the present day. This result provides a novel, high‑precision test of fundamental‑constant stability, complementary to previous constraints from recombination‑era CMB analyses. Future improvements in CMB measurements (e.g., CMB‑S4), more precise determinations of primordial deuterium, and refined nuclear reaction rates could tighten these bounds further, potentially probing sub‑percent variations in $m_e$ across cosmic time.