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 $Y_P$ is a powerful probe of cosmology.
Currently, $Y_P$ 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 and
He/H determinations for 10 EMPGs, combining the existing optical data and 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 $Y_P=0.2379^{+0.0031}_{-0.0030}$ by linear regression in
the (He/H)-(O/H) plane, where our observations increase the number of EMPGs
from 3 to 13 anchoring He/H of the most metal-poor gas in galaxies. Although
our $Y_P$ measurement and previous measurements are consistent, our result is
slightly (~ 1$\sigma$) smaller due to our EMPGs. Including the existing
primordial deuterium $D_P$ constraints, we estimate the effective number of
neutrino species to be $N_{eff}=2.41^{+0.19}_{-0.21}$ showing a > 2 $\sigma$
tension with the Standard Model value ($N_{eff}=3.046$), which may be a hint of
an asymmetry in electron-neutrino $\nu_e$ and anti-electron neutrino
$\bar{\nu}_e$. Allowing the degeneracy parameter of electron-neutrino $\xi_e$
to vary as well as $N_{eff}$ and the baryon-to-photon ratio $\eta$, we obtain
$\xi_e$ = $0.05^{+0.03}_{-0.03}$, $N_{eff}=3.22^{+0.33}_{-0.30}$, and
$\eta\times10^{10}=6.13^{+0.04}_{-0.04}$ from the $Y_P$ and $D_P$ measurements
with a prior of $\eta$ taken from Planck Collaboration et al. (2020). Our
constraints suggest a $\nu_e - \bar{\nu}_e$ asymmetry and allow for a high
value of $N_{eff}$ within the 1$\sigma$ level, which could mitigate the Hubble
tension.
