Primordial lepton asymmetries in the precision cosmology era: Current status and future sensitivities from BBN and the CMB

Using a new sample of extremely metal poor systems, the EMPRESS survey has recently reported a primordial helium abundance that is $3\sigma$ smaller than the prediction from the standard big bang nucleosynthesis (BBN) scenario. This measurement could be interpreted as a hint for a primordial lepton asymmetry in the electron neutrino flavor. Motivated by the EMPRESS results, we present a comprehensive analysis of the lepton asymmetry using measurements of the abundances of primordial elements, along with cosmic microwave background (CMB) data from Planck. Assuming that there is no dark radiation in our Universe, we find an electron neutrino chemical potential $\xi_{\nu_e} = 0.043 \pm 0.015$, which deviates from zero by $2.9\sigma$. If no assumption is made on the abundance of dark radiation in the Universe, the chemical potential is $\xi_{\nu_e} = 0.046 \pm 0.021$, which deviates from zero by $2.2\sigma$. We also find that this result is rather insensitive to the choice of nuclear reaction rates. If the true helium abundance corresponds to the EMPRESS central value, future CMB observations from the Simons Observatory and CMB-S4 will increase the significance for a nonzero lepton asymmetry to $4\sigma$ and $5\sigma$ respectively, assuming no dark radiation, or to $3\sigma$ when no assumption is made on the abundance of dark radiation.