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 the following $1\sigma$ bounds on $m_e$ in the early Universe: $m_e = 0.505^{+0.006}_{-0.007}$ MeV (for the NACRE II nuclear reaction network) or $m_e=0.509^{+0.005}_{-0.004}$ MeV (for the PRIMAT nuclear reaction network). These bounds have been derived by adopting the recent determination of the primordial Helium-4 abundance by the Large Binocular Telescope observations of 54 metal-poor H\,\textsc{ii} regions. If instead we adopt the Particle Data Book Helium-4 abundance, the bounds are: $m_e = 0.503^{+0.011}_{-0.015}$ MeV (NACRE II) or $m_e=0.521^{+0.009}_{-0.007}$ MeV (PRIMAT) The obtained allowed ranges are close to the present laboratory value at the level of $\sim 0.4\%-2\%$, depending on the dataset and nuclear network, thus supporting the constancy of the electron mass over cosmological timescales.