EMPRESS. VIII. A New Determination of Primordial He Abundance with Extremely Metal-Poor Galaxies: A Suggestion of the Lepton Asymmetry and Implications for the Hubble Tension

The primordial He abundance $Y_\mathrm{P}$ is a powerful probe of cosmology. Currently, $Y_\mathrm{P}$ is best determined by observations of metal-poor galaxies, while there are only a few known local extremely metal-poor ($<0.1 Z_\odot$) galaxies (EMPGs) having reliable He/H measurements with HeI$\lambda$10830 near-infrared (NIR) emission. Here we present deep Subaru NIR spectroscopy for 10 EMPGs. Combining the existing optical data, He/H values of 5 out of the 10 EMPGs are reliably derived by the Markov chain Monte Carlo algorithm. Adding the existing 3 EMPGs and 51 moderately metal-poor ($0.1-0.4 Z_\odot$) galaxies with reliable He/H estimates, we obtain $Y_\mathrm{P}=0.2370^{+0.0034}_{-0.0033}$ by linear regression in the $\mathrm{(He/H)}-\mathrm{(O/H)}$ plane, where we increase the number of EMPGs from 3 to 8 anchoring He/H of the most metal-poor gas in galaxies. Although our $Y_\mathrm{P}$ measurement and previous measurements are consistent, our result is slightly ($\sim 1\sigma$) smaller due to our EMPGs. With our $Y_\mathrm{P}$ and the existing primordial deuterium $D_\mathrm{P}$ measurement, we constrain the effective number of neutrino species $N_\mathrm{eff}$ and the baryon-to-photon ratio $\eta$ showing $\gtrsim 1-2\sigma$ tensions with the Standard Model and Planck Collaboration et al. (2020). Motivated by the tensions, we allow the degeneracy parameter of electron-neutrino $\xi_e$ to vary as well as $N_\mathrm{eff}$ and $\eta$. We obtain $\xi_e = 0.05^{+0.03}_{-0.02}$, $N_\mathrm{eff}=3.11^{+0.34}_{-0.31}$, and $\eta\times10^{10}=6.08^{+0.06}_{-0.06}$ from the $Y_\mathrm{P}$ and $D_\mathrm{P}$ measurements with a prior of $\eta$ taken from Planck Collaboration et al. (2020). Our constraints suggest a lepton asymmetry and allow for a high value of $N_\mathrm{eff}$ within the $1\sigma$ level, which could mitigate the Hubble tension.